Pin(2)-equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture · HackerPapers discussions

Pin(2)-equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture — mentioned by panic

Wed, 15 Apr 2015 23:50:30 GMT

Here is the actual paper: http://arxiv.org/pdf/1303.2354v4.pdf. It looks like this is their family of counter examples: A specific non-orientable five-dimensional manifold M5 with Sq1 ∆(M) ̸= 0 is constructed in [25]. Hence M5 is non-triangulable. To get non-orientable examples of non-triangulable manifolds in dimensions n > 5 we can take the product of M5 with the torus Tn−5. To get an orientable example in dimension 6 we can consider the non-orientable S1-bundle over M given by M ̃ ×Z/2 S1, where M ̃ → M is the oriented double cover; the total space of this bundle is orientable. To get…

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Pin(2)-equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture — mentioned by Retric

Wed, 15 Apr 2015 23:39:15 GMT

Seems odd that they did not provide a counter example. My suspicion there is an incorrect assumption for non fractal structures. PS: This is really one of those cases where a paper does not mean much. You really need to dig through http://arxiv.org/abs/1303.2354 and find the flaw as there is no peer review. Though it supposedly is going to show up in Journal of the AMS so it's not junk and probably worth diging into.

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Pin(2)-equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture — mentioned by pdpi

Tue, 13 Jan 2015 17:56:21 GMT

Seems that, though the posted article is new, the research in question is actually a couple of years old -- http://arxiv.org/abs/1303.2354

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