Poincaré dodecahedral space | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-02-18

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Homology_sphere


00:00:11 1 Poincaré homology sphere
00:00:42 1.1 Construction
00:01:16 1.2 Cosmology
00:02:36 2 Constructions and examples
00:03:19 3 Invariants
00:06:13 4 Applications
00:06:35 5 See also
00:08:07 6 References



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SUMMARY
=======
In algebraic topology, a homology sphere is an n-manifold X having the homology groups of an n-sphere, for some integer n ≥ 1. That is,

H0(X,Z) = Z = Hn(X,Z)and

Hi(X,Z) = {0} for all other i.Therefore X is a connected space, with one non-zero higher Betti number: bn. It does not follow that X is simply connected, only that its fundamental group is perfect (see Hurewicz theorem).
A rational homology sphere is defined similarly but using homology with rational coefficients.