Inner Product Spaces of the Homology Groups of Manifolds
نویسنده
چکیده
We discuss the inner product spaces of the middle homology groups of manifolds of dimensions 2 and 4. We prove that two compact 2-manifolds are homeomorphic if and only if the inner product spaces of their first homology groups are isomorphic. We outline a proof that every inner product space can be realized as the first homology group of some surface. We conclude by proving that two simply connected 4-manifolds are homotopy equivalent if and only if the inner product spaces of their second homology groups are isomorphic.
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