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In the applications and connections section it might also be nice to have a summary of the thread started by Mark Lackenby towards understanding the virtual Haken conjecture via coverings, weak irreducibility and group theory. In a similar vein it might also be nice to discuss Heegaard splittings via the complex of curves.
An important early theorem is the Reidemeister Singer theorem, this could lead into a discussion of Heegaard diagrams, which could make the whole affair a lot more concrete because you could draw some pictures of three-manifolds.
The link to Heegaard diagrams points to this page. I would be nice to have either a page on Heegaard diagrams or a full description of them here. —Preceding unsigned comment added by 128.119.47.189 ( talk) 18:59, 7 October 2010 (UTC)
Another fundamental result (and maybe one of the fundamental results about three manifolds) is Haken's lemma. Its completely missing from the discussion.
The biggest modern idea that goes without mention is Rubinstein's concept of a sweep, which had implications both in the study of minimal surfaces in three manifolds, and through the work of Rubinstein and Scharlemann on stabilizing Heegaard splittings on the theory of Heegaard splittings. -- User:Topoman
The paragraph "A Heegaard splitting is minimal or minimal genus if there is no other splitting of the ambient three-manifold of lower genus. The minimal value g of the splitting surface is the Heegaard genus of M." has an incorrect link to genus. It links to the biology term and not the mathematical term. I'm not experienced with editing Wikipedia articles and don't know how to fix this, but I hope somebody can. —Preceding unsigned comment added by 128.187.97.3 ( talk) 19:39, 5 November 2010 (UTC)
I wikilinked the section Heegaard Floer homology (Header and first occurence in the text) to the section of the same name in the article Floer homology - not being quite sure if this is 100% Wikipedia style. Rolf of: Erkabo 09:21, 14 November 2005 (UTC)
Could File:HeegaarsplitofSFS.PNG be used here? - Jochen Burghardt ( talk) 10:16, 29 March 2019 (UTC)
![]() | This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
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![]() | It is requested that a mathematical diagram or diagrams be
included in this article to
improve its quality. Specific illustrations, plots or diagrams can be requested at the
Graphic Lab. For more information, refer to discussion on this page and/or the listing at Wikipedia:Requested images. |
In the applications and connections section it might also be nice to have a summary of the thread started by Mark Lackenby towards understanding the virtual Haken conjecture via coverings, weak irreducibility and group theory. In a similar vein it might also be nice to discuss Heegaard splittings via the complex of curves.
An important early theorem is the Reidemeister Singer theorem, this could lead into a discussion of Heegaard diagrams, which could make the whole affair a lot more concrete because you could draw some pictures of three-manifolds.
The link to Heegaard diagrams points to this page. I would be nice to have either a page on Heegaard diagrams or a full description of them here. —Preceding unsigned comment added by 128.119.47.189 ( talk) 18:59, 7 October 2010 (UTC)
Another fundamental result (and maybe one of the fundamental results about three manifolds) is Haken's lemma. Its completely missing from the discussion.
The biggest modern idea that goes without mention is Rubinstein's concept of a sweep, which had implications both in the study of minimal surfaces in three manifolds, and through the work of Rubinstein and Scharlemann on stabilizing Heegaard splittings on the theory of Heegaard splittings. -- User:Topoman
The paragraph "A Heegaard splitting is minimal or minimal genus if there is no other splitting of the ambient three-manifold of lower genus. The minimal value g of the splitting surface is the Heegaard genus of M." has an incorrect link to genus. It links to the biology term and not the mathematical term. I'm not experienced with editing Wikipedia articles and don't know how to fix this, but I hope somebody can. —Preceding unsigned comment added by 128.187.97.3 ( talk) 19:39, 5 November 2010 (UTC)
I wikilinked the section Heegaard Floer homology (Header and first occurence in the text) to the section of the same name in the article Floer homology - not being quite sure if this is 100% Wikipedia style. Rolf of: Erkabo 09:21, 14 November 2005 (UTC)
Could File:HeegaarsplitofSFS.PNG be used here? - Jochen Burghardt ( talk) 10:16, 29 March 2019 (UTC)