Timeline for Any PL-homology-manifold is homotopy equivalent to a manifold

8 events

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Dec 15, 2015 at 16:54	comment	added	Mikhail Katz		Did you check Hillman's papers on higher-dimensional spaces?
Dec 15, 2015 at 16:50	comment	added	Misha		@ε-δ: You are right, I missed the assumption that the space is a PL homology manifold. Then, indeed, in dimension 3 they all are ordinary PL manifolds.
Dec 15, 2015 at 16:10	comment	added	ε-δ		en.wikipedia.org/wiki/Homology_manifold Please correct me if I am wrong: the link of vertex in h-manifold has to be homological sphere, so if dimension is 3 it has to be 2-sphere, so it was a manifold.
Dec 15, 2015 at 16:05	comment	added	Mikhail Katz		@ε-δ, What do you mean by a "homology manifold"?
Dec 15, 2015 at 16:03	comment	added	ε-δ		Sorry, I did not get it — are you trying to say that there is a counterexample in dimension 3? — all 3-dimensional homological PL-mainifolds are manifolds, aren't they?
Dec 15, 2015 at 8:00	comment	added	Mikhail Katz		@Misha, thanks for doing my work for me :-)
Dec 14, 2015 at 17:42	comment	added	Misha		Indeed: The paper J. Hillman, An indecomposable PD3-complex whose fundamental group has infinitely many ends, Math. Proc. Cambridge Philos. Soc. 138 (2005), 55–57, contains an example whose fundamental group is not isomorphic to a 3-manifold group. Somebody (C.B.Thomas?) also had an earlier example with finite fundamental group.
Dec 14, 2015 at 15:26	history	answered	Mikhail Katz	CC BY-SA 3.0