Last Updated
：2025/11/27
Poincaré space
Noun
Japanese Meaning
（位相幾何学）n次元の位相空間で、n次ホモロジー群における特別な要素 µ を持ち、任意のk次コホモロジー群の要素とのカップ積により、(n − k)次コホモロジー群と同型写像が得られる空間。
（ plural ）
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(topology) An n-dimensional topological space with a distinguished element µ of its nth homology group such that taking the cap product with an element of the kth cohomology group yields an isomorphism to the (n − k)th cohomology group.
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Poincaré space
A Poincaré space often serves as an algebraic-topology analogue of a manifold, because its distinguished fundamental class μ induces cap-product isomorphisms between cohomology groups in complementary dimensions.
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A Poincaré space often serves as an algebraic-topology analogue of a manifold, because its distinguished fundamental class μ induces cap-product isomorphisms between cohomology groups in complementary dimensions.
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