Last Updated：2025/11/27
Sentence
そのようなn次元位相空間は、n次同調群の特別な元μを持ち、k次コホモロジー群の元とのキャップ積により(n − k)次コホモロジー群への同型を与えるため、代数的位相幾何学で多様体のモデルとしてしばしば用いられる。
Quizzes for review
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.
See correct answer
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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Related words
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。
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