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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Poincaré space ： ウィキペディア英語版 Poincaré space In algebraic topology, a Poincaré space is an ''n''-dimensional topological space with a distinguished element ''µ'' of its ''n''th homology group such that taking the cap product with an element of the ''k''th cohomology group yields an isomorphism to the (''n'' − ''k'')th homology group. The space is essentially one for which Poincaré duality is valid; more precisely, one whose singular chain complex forms a Poincaré complex with respect to the distinguished element ''µ''. For example, any closed, orientable, connected manifold ''M'' is a Poincaré space, where the distinguished element is the fundamental class $().$ Poincaré spaces are used in surgery theory to analyze and classify manifolds. Not every Poincaré space is a manifold, but the difference can be studied, first by having a normal map from a manifold, and then via obstruction theory. ==Other uses== Sometimes, ''Poincaré space'' means a homology sphere with non-trivial fundamental group—for instance, the Poincaré dodecahedral space in 3 dimensions. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Poincaré space」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.