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Mathematics B‑class High‑priority

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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)

This is the 10/8 theorem, theorem 2 of a paper of Donaldson, The orientation of Yang-Mills moduli spaces and 4-manifolds topology, J. Diff. Geom. 26 (1987), 397–428.. Orthografer 17:59, 30 May 2007 (UTC)

I looked up that theorem, and it does not say this. That theorem assumes the positive part has rank 1 or 2. There is a relevant theorem of Furuta, but it's not quite as strong as stated. --Dylan Thurston (talk) 20:45, 8 September 2009 (UTC)

My mistake, Furuta's theorem is precisely what's written. Reference added. --Dylan Thurston (talk) 00:20, 10 September 2009 (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)

I can give you a meta-reference: Thurston's book mentions this fact and should have some references for it. --C S (talk) 23:15, 31 July 2008 (UTC)

That book only mentions results for dimensions 3 or less. Kirby and Siebenmann's book is a better guess; however, their techniques only apply in dimensions 5 and higher, so are not useful for this article. They refer to Cerf's 1959 paper for dimensions 4 and less, but that seems to be a mistake as far as I can tell. --Dylan Thurston (talk) 20:45, 8 September 2009 (UTC)

Classification of homeomorphic manifolds

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. linas (talk) 17:56, 26 November 2011 (UTC)

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