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It seems that the atmosphere got a bit too heated up for a fruitful collaboration. So, I propose we all stop editing the article and the talk page for a week, calm down, and come back here on 22:23, 2 August 2005 (UTC).
Old talk page is in talk:manifold/rewrite/freezer
Thank you, Jitse Niesen ( talk) 22:24, 26 July 2005 (UTC)
Please note that it looks as if manifold/rewrite has been merged into manifold by Deryck Chan (no, don't ask me why and what, I discovered this by accident). Oleg Alexandrov 03:22, 4 August 2005 (UTC)
I think that these two sections overlap in their content too much and are causing the article to look cluttered. Indeed, most of the examples deal directly with constructions. I prefer to look at them as examples of constructions rather than standalone examples. A new "construction" which just appeared due to Joshua deals with the double line (non-Hausdorff); I'm wondering how technically complicated this construction is to a newcomer? - Gauge 06:58, 5 August 2005 (UTC)
I like the new picture by KSmrq. I thought putting everything in one picture would make it too cluttered, but I now see I was wrong. Two remarks though: I think the lines are a bit too thick, and the domains of the charts in the picture do not match with the description in the text, where all charts cover half of the circle (I understand that one needs to leave a gap between the domains of the blue and green map in the picture, but I wonder whether the gap can be shrunk). -- Jitse Niesen ( talk) 12:08, 5 August 2005 (UTC)
Ad 1. I understand what you're getting at; in fact, I prodded Oleg to thicken lines for the same reason. However, I still think the lines are probably too thick, especially since the colours are not essential. However, it is a detail, and as you say, creating pictures costs a lot of time, perhaps better spent on other matters.
Ad 2. Fair enough. My comment was mainly in case you hadn't thought about it (I hope you don't mind). Jitse Niesen ( talk) 21:17, 5 August 2005 (UTC)
See Talk:Manifold#How_far_till_this_is_done.3F. Wonder if there is any way to merge the histories too. Oleg Alexandrov 04:53, 9 August 2005 (UTC)
"A manifold can be characterised as looking like Euclidean space, or some other relatively simple space, in a close-up view."
"A manifold can be characterised as looking like a relatively simple space in a close-up view."
The cone is an bad choice of counterexample for the introduction, for two reasons. First, the reader does not know if we mean an object with a circular cross section tapering to a point, or a full quadric "double cone" as is common in geometry, or something else. (And neither do I!) Second, the point may be a problem for a differentiable manifold, but a (half-)cone is a perfectly good topological manifold, homeomorphic to a disc. KSmrq 01:01, 2005 August 10 (UTC)
Further inspection reveals more problems. Consider
"[T]he surface of the Earth looks flat when you are standing on it."
Somebody ought to get outside more! Almost nowhere on Earth is terrain that flat. What's a reader in Switzerland or Alaska going to think? If we're appealing to intuition based on everyday experience, we blew it.
Also, I see mention of different kinds of manifolds, but my remark about manifolds-with-boundary has disappeared. These are far too important to omit. KSmrq 01:20, 2005 August 10 (UTC)
OK, I've leveraged Markus' flat Earth as proposed. Meanwhile, I spotted this non sequitur:
"Note that T is simply a function between open intervals, so we know what it means for T to be differentiable."
Right; as if high school students know all about open intervals and differentiability! I'm thinking we should remove this from the introduction and introduce it later. Either that or flag it as a comment for advanced readers. KSmrq 03:10, 2005 August 11 (UTC)
I seem to be attempting a series of small edits, and I thought it best to say a word about them as I go.
I've added a couple of sketchy paragraphs to the circle example that probably don't belong exactly there, but since I don't presently have a better home, there they are. The flow of the text is roughly thus:
As noted, this overloads the circle example; but I think the progression may be helpful.
Whenever I give a talk or write a paper, I concentrate on clearly conveying one idea. I expect to see that reflected in the table of contents. The organization of this page doesn't yet have that focus and clarity. A standard rhetorical device is to organize in threes, as in the famous beginning, middle, end dictum. For example, common advice for talks is: (1) tell them what you're going to tell them, (2) tell them, (3) tell them what you told them. Also popular are balanced pairs, as in "this and that".
Just so you know where I'm headed. KSmrq 03:48, 2005 August 10 (UTC)
[Copied from User talk:KSmrq]
By the way, it took me pretty long to grasp the above example [the slope chart picture]. Maybe something like
<?xml version="1.0" encoding="utf-8"?> <svg width="1014" height="592"> <ellipse cx="505.12020519966717" cy="296.47827308529054" rx="95.72940535020797" ry="95.72940535020797" style="stroke:rgb(0,0,0);fill:none;stroke-width:3"/> <line x1="409.3907998494592" y1="296.4782730852906" x2="600.8496105498751" y2="105.0194623848746" style="stroke:rgb(180,0,0);stroke-width:1"/> <line x1="600.8496105498751" y1="105.0194623848746" x2="594.0" y2="118.0" style="stroke:rgb(180,0,0);stroke-width:1"/> <line x1="600.8496105498751" y1="105.0194623848746" x2="587.0" y2="112.0" style="stroke:rgb(180,0,0);stroke-width:1"/> <line x1="409.3907998494592" y1="296.4782730852906" x2="600.8496105498751" y2="392.2076784354985" style="stroke:rgb(0,0,178);stroke-width:1"/> <line x1="600.8496105498751" y1="392.2076784354985" x2="586.0" y2="390.0" style="stroke:rgb(0,0,178);stroke-width:1"/> <line x1="600.8496105498751" y1="392.2076784354985" x2="590.0" y2="382.0" style="stroke:rgb(0,0,178);stroke-width:1"/> <path d="M 406.0 293.0 H 411.0 V 298.0 H 406.0 Z" style="fill:rgb(0,124,0);stroke:rgb(0,124,0);stroke-width:1"/> <line x1="601.0" y1="1309.0" x2="601.0" y2="-718.0" style="stroke:rgb(0,0,0);stroke-width:1"/> <path d="M 598.0 102.0 H 603.0 V 107.0 H 598.0 Z" style="fill:rgb(180,0,0);stroke:rgb(180,0,0);stroke-width:1"/> <text x="606.8496105498751" y="123.0194623848746" style="font-size:0;fill:rgb(180,0,0);font-weight:normal">1</text><path d="M 598.0 389.0 H 603.0 V 394.0 H 598.0 Z" style="fill:rgb(0,0,178);stroke:rgb(0,0,178);stroke-width:1"/> <text x="606.8496105498751" y="410.2076784354985" style="font-size:0;fill:rgb(0,0,178);font-weight:normal">1/2</text><path d="M 502.0 198.0 H 507.0 V 203.0 H 502.0 Z" style="fill:rgb(180,0,0);stroke:rgb(180,0,0);stroke-width:1"/> <path d="M 560.0 370.0 H 565.0 V 375.0 H 560.0 Z" style="fill:rgb(0,0,178);stroke:rgb(0,0,178);stroke-width:1"/> </svg>
or
<?xml version="1.0" encoding="utf-8"?> <svg width="1014" height="592"> <ellipse cx="570.0" cy="296.0" rx="3.0" ry="3.0" style="stroke:rgb(0,124,124);stroke-width:1;fill:none"/> <ellipse cx="507.0" cy="296.0" rx="63.375" ry="63.375" style="stroke:rgb(0,0,0);fill:none;stroke-width:1"/> <path d="M 478.0 235.0 H 483.0 V 240.0 H 478.0 Z" style="fill:rgb(0,0,0);stroke:rgb(0,0,0);stroke-width:1"/> <line x1="507.0" y1="1309.0" x2="507.0" y2="-718.0" style="stroke:rgb(0,0,0);stroke-width:1"/> <ellipse cx="507.0" cy="255.0" rx="3.0" ry="3.0" style="fill:rgb(180,0,0)"/> <ellipse cx="507.0" cy="255.0" rx="3.0" ry="3.0" style="stroke:rgb(180,0,0);stroke-width:1;fill:none"/> <ellipse cx="444.0" cy="296.0" rx="3.0" ry="3.0" style="stroke:rgb(0,124,124);stroke-width:1;fill:none"/> <ellipse cx="507.0" cy="199.0" rx="3.0" ry="3.0" style="fill:rgb(0,0,178)"/> <ellipse cx="507.0" cy="199.0" rx="3.0" ry="3.0" style="stroke:rgb(0,0,178);stroke-width:1;fill:none"/> <line x1="443.625" y1="296.0" x2="481.41930190822734" y2="238.0170843253154" style="stroke:rgb(153,153,224);stroke-width:1"/> <line x1="443.625" y1="296.0" x2="507.0" y2="198.7719234024745" style="stroke:rgb(0,0,178);stroke-width:1"/> <line x1="507.0" y1="198.7719234024745" x2="503.0" y2="213.0" style="stroke:rgb(0,0,178);stroke-width:1"/> <line x1="507.0" y1="198.7719234024745" x2="495.0" y2="208.0" style="stroke:rgb(0,0,178);stroke-width:1"/> <line x1="570.375" y1="296.0" x2="481.41930190822734" y2="238.0170843253154" style="stroke:rgb(225,153,153);stroke-width:1"/> <line x1="570.375" y1="296.0" x2="507.0" y2="254.69104104953345" style="stroke:rgb(180,0,0);stroke-width:1"/> <line x1="507.0" y1="254.69104104953345" x2="521.0" y2="259.0" style="stroke:rgb(180,0,0);stroke-width:1"/> <line x1="507.0" y1="254.69104104953345" x2="516.0" y2="266.0" style="stroke:rgb(180,0,0);stroke-width:1"/> </svg>
might be easier to understand.
Sorry for cluttering your talk page. The SVGs don't use all the things you mentioned above, but just illustrate what I'm thinking about. Markus Schmaus 21:55, 7 August 2005 (UTC)
I understand your point and agree with your reasons. But is the slope chart an ideal example for a chart which is not a geometric projection, as it is equivalent to the stereographic projection? What about the angle chart? It cannot be understood as a geometric projection. Or if this is too easy what about the signed distance between a point and (1, 0) in R2? Markus Schmaus 13:16, 10 August 2005 (UTC)
Under Intrinsic vs. Extrinsic Views:
This makes no sense to me. What "line" are we talking about here?
On a different note, we really should try to clarify the relationship between sheaves and atlases if we are going to include varieties and schemes as examples of manifolds according to the definition given here. A scheme is locally built up of affine schemes, which are topological spaces with the Zariski topology, and the atlas would consist of maps that are (open?) immersions of affines. What are the transition maps? I'm guessing that they should be regular morphisms, but I don't know enough geometry yet to know for sure. Btw, the notion of exclusively using something like "Euclidean space" goes out the window in these situations because affine schemes almost never look like Euclidean spaces (not Hausdorff, for instance).
Finally, according to the simple space definition, orbifolds are not generalizations of manifolds... they are just manifolds, where we admit quotients of Euclidean space by finite group actions as "simple" enough. - Gauge 03:35, 11 August 2005 (UTC)
It seems now would be the time to shorten the table of contents to a reasonable length. In the construction section, I have difficulty distinguishing immediately between the "Ideas" and the "Examples of the Ideas" because, despite the use of indentation in the examples themselves, the headers are still on the left since they are sections. Ideally, we could indent the headers as well. Does anyone know how to do this? - Gauge 03:48, 11 August 2005 (UTC)
This section could be expanded to "Local topological criteria" or some similar title and refer not only to Hausdorff-ness, but also paracompactness (useful for partitions of unity), local metrizability, and so on. In other words, brief explanations of any local "niceness" conditions could go here. I'm not going to be around for the next week, so feel free to overwrite the old article while I am away. - Gauge 00:55, 13 August 2005 (UTC)
I'm glad to see all the hard work that has gone into improving this article. Are we ready to replace the original yet? Either that or very close I think. Anything worthwhile that is not yet incorporated should be added to this version. But it probably already has a home here at or one of the other two articles. Talking about those, I see no activity there. How come? I also think the time has come to do a request for comments or whatever it's called. -- MarSch 15:41, 14 August 2005 (UTC)
I can't see any independent "charts" construction, in fact the sphere in the example is constructed as zeros of x2 + y2 + z2 - 1. Markus Schmaus 12:08, 15 August 2005 (UTC)
-- MarSch 12:43, 16 August 2005 (UTC)
[moved by Markus Schmaus]
-- MarSch 12:43, 16 August 2005 (UTC)
Current intro reads:
In mathematics, a manifold generalizes the idea of a surface. Technically, it can be constructed using multiple overlapping pieces to form a whole and is, in this sense, like a patchwork. On a small scale manifolds are always simple; on a large scale, they have rich flexibility.
I also dislike the "In the remainder of this article...". Completely unnecessary. I would like to integrate the parts about terminology coming from cartography, which is another valuable metaphor, into the part currently headed "introduction" and remove that heading. I think we should fully exploit the cartography metaphor, by covering the Earth with some charts (as I did in a previous version). Please comment. -- MarSch 13:08, 16 August 2005 (UTC)
I would agree with KSmrq about letting the introduction stand for now. There is a lot of work to be done below. Oleg Alexandrov 21:12, 20 August 2005 (UTC)
Now on to more productive topics. When you say "it looks finished but isn't", I agree, and have said so previously on this page. The question is, what to do about it? This is one area where wiki collaboration is awkward, because reorganization is not local edits, but an all-or-nothing commitment which is either accepted or reverted. Nevertheless, I'd be delighted if we can work together and bring this rewrite to a satisfactory conclusion. To that end, can you provide a link to the version of manifold that you consider your best effort, so we have a common point of reference? I'll read that and compare it to the state of the rewrite. Also, it might help if you could (briefly) state which topics or aspects of presentation are most important in your view. Here's my concept:
I want an article that's just long enough to clearly say what it has to say. It should flow naturally from start to finish. It should be engaging, but not sloppy. It should be well illustrated. (Also, I'd like to complete my part in this quite soon.)
So, maybe that's a lot to ask, and maybe is not exactly what others have in mind. For example, currently the rewrite includes a long section on construction, with many examples; I'm inclined to spin that off into a separate article. Everyone, do we agree on goals? -- KSmrq 13:34, 2005 August 18 (UTC)
I am not a native speaker of English, and this is why I have these maybe naive questions.
The text currenty says:
Should these be respectively
That is, should there be the articles "an" and "the" in places? Thanks. Oleg Alexandrov 17:30, 17 August 2005 (UTC)
I agree with Jitse that differentiable transition maps is all that is required (and all that makes sense/has meaning). The charts are declared to be C^k exactly when the transitions maps are C^k. Perhaps an example to enlighten us of what you mean?-- MarSch 11:33, 21 August 2005 (UTC)
It all depends on what structure you insist on inheriting from R^n. (KSmrq, I know you didn't say this, I was just thinking of what might be happening in your head.) Continuing on that line an everywhere non-continuous height function can be used. The only requirement on the charts is that they be invertible, thus bijections. Every structure that you want (including topology) can then be transported. The cone as constructed by Jitse is a topological submanifold of the topological manifold R^3, but it is not a differentiable submanifold, even though it is a differentiable manifold. -- MarSch 15:29, 28 August 2005 (UTC)
Do we really need the second sphere example? the one with two charts. It's just stereographic projection, but somehow I find it much less enlightening than the first construction. If there is no strong reason to keep it here I propose to move it to circle.-- MarSch 12:30, 23 August 2005 (UTC)
I just made some edits to the page, including changing the extra constructions into short examples and leaving out the technical details, which were already present on the respective article pages ( torus, real projective space, cylinder, Klein bottle), with the exception of the latter two (I will fill these in as I find time; they are on my talk page if you'd like to do it yourself). Besides those things, the only other things that I see lacking with the article currently are:
Happy editing, Gauge 05:27, 24 August 2005 (UTC)
It's time to move Manifold/rewrite to Manifold. Markus Schmaus 19:55, 7 September 2005 (UTC)
It's time to move Manifold/rewrite to Manifold. Markus Schmaus 19:56, 7 September 2005 (UTC)
It's time to move Manifold/rewrite to Manifold. Oleg Alexandrov 21:38, 7 September 2005 (UTC)
I extend my thanks to everyone who has contributed to make this article what it is today. Merge! - Gauge 03:41, 8 September 2005 (UTC)
I concur. We can do two things to preserve history of the old page. Move it to manifold/old, or merge histories from the moment of the split (we loose history on old version after split). move -- MarSch 15:13, 8 September 2005 (UTC)
I implemented Jitse's suggestion. The old article is manifold/old, and its talk is talk:manifold/old. Also see talk:manifold/rewrite/freezer. If people feel like merging the histories later, it can still be done. Oleg Alexandrov ( talk) 13:14, 18 October 2005 (UTC)
![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | Archive 2 | Archive 3 | Archive 4 | Archive 5 |
It seems that the atmosphere got a bit too heated up for a fruitful collaboration. So, I propose we all stop editing the article and the talk page for a week, calm down, and come back here on 22:23, 2 August 2005 (UTC).
Old talk page is in talk:manifold/rewrite/freezer
Thank you, Jitse Niesen ( talk) 22:24, 26 July 2005 (UTC)
Please note that it looks as if manifold/rewrite has been merged into manifold by Deryck Chan (no, don't ask me why and what, I discovered this by accident). Oleg Alexandrov 03:22, 4 August 2005 (UTC)
I think that these two sections overlap in their content too much and are causing the article to look cluttered. Indeed, most of the examples deal directly with constructions. I prefer to look at them as examples of constructions rather than standalone examples. A new "construction" which just appeared due to Joshua deals with the double line (non-Hausdorff); I'm wondering how technically complicated this construction is to a newcomer? - Gauge 06:58, 5 August 2005 (UTC)
I like the new picture by KSmrq. I thought putting everything in one picture would make it too cluttered, but I now see I was wrong. Two remarks though: I think the lines are a bit too thick, and the domains of the charts in the picture do not match with the description in the text, where all charts cover half of the circle (I understand that one needs to leave a gap between the domains of the blue and green map in the picture, but I wonder whether the gap can be shrunk). -- Jitse Niesen ( talk) 12:08, 5 August 2005 (UTC)
Ad 1. I understand what you're getting at; in fact, I prodded Oleg to thicken lines for the same reason. However, I still think the lines are probably too thick, especially since the colours are not essential. However, it is a detail, and as you say, creating pictures costs a lot of time, perhaps better spent on other matters.
Ad 2. Fair enough. My comment was mainly in case you hadn't thought about it (I hope you don't mind). Jitse Niesen ( talk) 21:17, 5 August 2005 (UTC)
See Talk:Manifold#How_far_till_this_is_done.3F. Wonder if there is any way to merge the histories too. Oleg Alexandrov 04:53, 9 August 2005 (UTC)
"A manifold can be characterised as looking like Euclidean space, or some other relatively simple space, in a close-up view."
"A manifold can be characterised as looking like a relatively simple space in a close-up view."
The cone is an bad choice of counterexample for the introduction, for two reasons. First, the reader does not know if we mean an object with a circular cross section tapering to a point, or a full quadric "double cone" as is common in geometry, or something else. (And neither do I!) Second, the point may be a problem for a differentiable manifold, but a (half-)cone is a perfectly good topological manifold, homeomorphic to a disc. KSmrq 01:01, 2005 August 10 (UTC)
Further inspection reveals more problems. Consider
"[T]he surface of the Earth looks flat when you are standing on it."
Somebody ought to get outside more! Almost nowhere on Earth is terrain that flat. What's a reader in Switzerland or Alaska going to think? If we're appealing to intuition based on everyday experience, we blew it.
Also, I see mention of different kinds of manifolds, but my remark about manifolds-with-boundary has disappeared. These are far too important to omit. KSmrq 01:20, 2005 August 10 (UTC)
OK, I've leveraged Markus' flat Earth as proposed. Meanwhile, I spotted this non sequitur:
"Note that T is simply a function between open intervals, so we know what it means for T to be differentiable."
Right; as if high school students know all about open intervals and differentiability! I'm thinking we should remove this from the introduction and introduce it later. Either that or flag it as a comment for advanced readers. KSmrq 03:10, 2005 August 11 (UTC)
I seem to be attempting a series of small edits, and I thought it best to say a word about them as I go.
I've added a couple of sketchy paragraphs to the circle example that probably don't belong exactly there, but since I don't presently have a better home, there they are. The flow of the text is roughly thus:
As noted, this overloads the circle example; but I think the progression may be helpful.
Whenever I give a talk or write a paper, I concentrate on clearly conveying one idea. I expect to see that reflected in the table of contents. The organization of this page doesn't yet have that focus and clarity. A standard rhetorical device is to organize in threes, as in the famous beginning, middle, end dictum. For example, common advice for talks is: (1) tell them what you're going to tell them, (2) tell them, (3) tell them what you told them. Also popular are balanced pairs, as in "this and that".
Just so you know where I'm headed. KSmrq 03:48, 2005 August 10 (UTC)
[Copied from User talk:KSmrq]
By the way, it took me pretty long to grasp the above example [the slope chart picture]. Maybe something like
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or
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might be easier to understand.
Sorry for cluttering your talk page. The SVGs don't use all the things you mentioned above, but just illustrate what I'm thinking about. Markus Schmaus 21:55, 7 August 2005 (UTC)
I understand your point and agree with your reasons. But is the slope chart an ideal example for a chart which is not a geometric projection, as it is equivalent to the stereographic projection? What about the angle chart? It cannot be understood as a geometric projection. Or if this is too easy what about the signed distance between a point and (1, 0) in R2? Markus Schmaus 13:16, 10 August 2005 (UTC)
Under Intrinsic vs. Extrinsic Views:
This makes no sense to me. What "line" are we talking about here?
On a different note, we really should try to clarify the relationship between sheaves and atlases if we are going to include varieties and schemes as examples of manifolds according to the definition given here. A scheme is locally built up of affine schemes, which are topological spaces with the Zariski topology, and the atlas would consist of maps that are (open?) immersions of affines. What are the transition maps? I'm guessing that they should be regular morphisms, but I don't know enough geometry yet to know for sure. Btw, the notion of exclusively using something like "Euclidean space" goes out the window in these situations because affine schemes almost never look like Euclidean spaces (not Hausdorff, for instance).
Finally, according to the simple space definition, orbifolds are not generalizations of manifolds... they are just manifolds, where we admit quotients of Euclidean space by finite group actions as "simple" enough. - Gauge 03:35, 11 August 2005 (UTC)
It seems now would be the time to shorten the table of contents to a reasonable length. In the construction section, I have difficulty distinguishing immediately between the "Ideas" and the "Examples of the Ideas" because, despite the use of indentation in the examples themselves, the headers are still on the left since they are sections. Ideally, we could indent the headers as well. Does anyone know how to do this? - Gauge 03:48, 11 August 2005 (UTC)
This section could be expanded to "Local topological criteria" or some similar title and refer not only to Hausdorff-ness, but also paracompactness (useful for partitions of unity), local metrizability, and so on. In other words, brief explanations of any local "niceness" conditions could go here. I'm not going to be around for the next week, so feel free to overwrite the old article while I am away. - Gauge 00:55, 13 August 2005 (UTC)
I'm glad to see all the hard work that has gone into improving this article. Are we ready to replace the original yet? Either that or very close I think. Anything worthwhile that is not yet incorporated should be added to this version. But it probably already has a home here at or one of the other two articles. Talking about those, I see no activity there. How come? I also think the time has come to do a request for comments or whatever it's called. -- MarSch 15:41, 14 August 2005 (UTC)
I can't see any independent "charts" construction, in fact the sphere in the example is constructed as zeros of x2 + y2 + z2 - 1. Markus Schmaus 12:08, 15 August 2005 (UTC)
-- MarSch 12:43, 16 August 2005 (UTC)
[moved by Markus Schmaus]
-- MarSch 12:43, 16 August 2005 (UTC)
Current intro reads:
In mathematics, a manifold generalizes the idea of a surface. Technically, it can be constructed using multiple overlapping pieces to form a whole and is, in this sense, like a patchwork. On a small scale manifolds are always simple; on a large scale, they have rich flexibility.
I also dislike the "In the remainder of this article...". Completely unnecessary. I would like to integrate the parts about terminology coming from cartography, which is another valuable metaphor, into the part currently headed "introduction" and remove that heading. I think we should fully exploit the cartography metaphor, by covering the Earth with some charts (as I did in a previous version). Please comment. -- MarSch 13:08, 16 August 2005 (UTC)
I would agree with KSmrq about letting the introduction stand for now. There is a lot of work to be done below. Oleg Alexandrov 21:12, 20 August 2005 (UTC)
Now on to more productive topics. When you say "it looks finished but isn't", I agree, and have said so previously on this page. The question is, what to do about it? This is one area where wiki collaboration is awkward, because reorganization is not local edits, but an all-or-nothing commitment which is either accepted or reverted. Nevertheless, I'd be delighted if we can work together and bring this rewrite to a satisfactory conclusion. To that end, can you provide a link to the version of manifold that you consider your best effort, so we have a common point of reference? I'll read that and compare it to the state of the rewrite. Also, it might help if you could (briefly) state which topics or aspects of presentation are most important in your view. Here's my concept:
I want an article that's just long enough to clearly say what it has to say. It should flow naturally from start to finish. It should be engaging, but not sloppy. It should be well illustrated. (Also, I'd like to complete my part in this quite soon.)
So, maybe that's a lot to ask, and maybe is not exactly what others have in mind. For example, currently the rewrite includes a long section on construction, with many examples; I'm inclined to spin that off into a separate article. Everyone, do we agree on goals? -- KSmrq 13:34, 2005 August 18 (UTC)
I am not a native speaker of English, and this is why I have these maybe naive questions.
The text currenty says:
Should these be respectively
That is, should there be the articles "an" and "the" in places? Thanks. Oleg Alexandrov 17:30, 17 August 2005 (UTC)
I agree with Jitse that differentiable transition maps is all that is required (and all that makes sense/has meaning). The charts are declared to be C^k exactly when the transitions maps are C^k. Perhaps an example to enlighten us of what you mean?-- MarSch 11:33, 21 August 2005 (UTC)
It all depends on what structure you insist on inheriting from R^n. (KSmrq, I know you didn't say this, I was just thinking of what might be happening in your head.) Continuing on that line an everywhere non-continuous height function can be used. The only requirement on the charts is that they be invertible, thus bijections. Every structure that you want (including topology) can then be transported. The cone as constructed by Jitse is a topological submanifold of the topological manifold R^3, but it is not a differentiable submanifold, even though it is a differentiable manifold. -- MarSch 15:29, 28 August 2005 (UTC)
Do we really need the second sphere example? the one with two charts. It's just stereographic projection, but somehow I find it much less enlightening than the first construction. If there is no strong reason to keep it here I propose to move it to circle.-- MarSch 12:30, 23 August 2005 (UTC)
I just made some edits to the page, including changing the extra constructions into short examples and leaving out the technical details, which were already present on the respective article pages ( torus, real projective space, cylinder, Klein bottle), with the exception of the latter two (I will fill these in as I find time; they are on my talk page if you'd like to do it yourself). Besides those things, the only other things that I see lacking with the article currently are:
Happy editing, Gauge 05:27, 24 August 2005 (UTC)
It's time to move Manifold/rewrite to Manifold. Markus Schmaus 19:55, 7 September 2005 (UTC)
It's time to move Manifold/rewrite to Manifold. Markus Schmaus 19:56, 7 September 2005 (UTC)
It's time to move Manifold/rewrite to Manifold. Oleg Alexandrov 21:38, 7 September 2005 (UTC)
I extend my thanks to everyone who has contributed to make this article what it is today. Merge! - Gauge 03:41, 8 September 2005 (UTC)
I concur. We can do two things to preserve history of the old page. Move it to manifold/old, or merge histories from the moment of the split (we loose history on old version after split). move -- MarSch 15:13, 8 September 2005 (UTC)
I implemented Jitse's suggestion. The old article is manifold/old, and its talk is talk:manifold/old. Also see talk:manifold/rewrite/freezer. If people feel like merging the histories later, it can still be done. Oleg Alexandrov ( talk) 13:14, 18 October 2005 (UTC)