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Does anyone have a reference for the following claim maid in this article. (I thought it is still open).
Take a sum of m copies of II_{1,1} and 2n copies of E_8. If m \le 2n, then "Donaldson and Furuta proved" that no smooth structure exists. Katzmik 09:23, 9 May 2007 (UTC)
Changed priority to top because our universe is at least 4 manifold! We need to understant this Daniel de França ( talk) 19:21, 12 March 2008 (UTC)
Can someone give a reference about statement "For manifolds of dimension at most 6, any piecewise linear (PL) structure can be smoothed in an essentially unique way"? Omar.zanusso ( talk) 15:10, 30 May 2008 (UTC)
Article currently has a huge hole in it: a discussion of the non-classifiability of 4-manifolds, the thm by Markov (more precisely, "there is no algorithm for classifying 4-D manifolds") see e.g. http://www.mathkb.com/Uwe/Forum.aspx/math/13873/4-manifold-classification for references. Current article is even misleading: right from the get-go, just a few sentences in, it starts talking about "Freedman's classification", which seems to imply that they are classifiable! Should state first, that, in general, they're not, but that there are certain special cases which are (i.e. the Freedman case). linas ( talk) 17:56, 26 November 2011 (UTC)
![]() | This ![]() It is of interest to the following WikiProjects: | ||||||||||
|
Does anyone have a reference for the following claim maid in this article. (I thought it is still open).
Take a sum of m copies of II_{1,1} and 2n copies of E_8. If m \le 2n, then "Donaldson and Furuta proved" that no smooth structure exists. Katzmik 09:23, 9 May 2007 (UTC)
Changed priority to top because our universe is at least 4 manifold! We need to understant this Daniel de França ( talk) 19:21, 12 March 2008 (UTC)
Can someone give a reference about statement "For manifolds of dimension at most 6, any piecewise linear (PL) structure can be smoothed in an essentially unique way"? Omar.zanusso ( talk) 15:10, 30 May 2008 (UTC)
Article currently has a huge hole in it: a discussion of the non-classifiability of 4-manifolds, the thm by Markov (more precisely, "there is no algorithm for classifying 4-D manifolds") see e.g. http://www.mathkb.com/Uwe/Forum.aspx/math/13873/4-manifold-classification for references. Current article is even misleading: right from the get-go, just a few sentences in, it starts talking about "Freedman's classification", which seems to imply that they are classifiable! Should state first, that, in general, they're not, but that there are certain special cases which are (i.e. the Freedman case). linas ( talk) 17:56, 26 November 2011 (UTC)