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Homotopy sphere
In algebraic topology, a branch of mathematics, a homotopy sphere is a manifold homotopy equivalent to an n-sphere. It thus has the same homotopy groups, and a fortiori the same homology groups, as a sphere. So every homotopy sphere is an homology sphere.
The generalized Poincaré conjecture is that any homotopy sphere is a sphere; see the article Poincaré conjecture for more details.
See also
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details