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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 Cobordism ring ： ウィキペディア英語版 Cobordism ring In mathematics, the oriented cobordism ring is a ring where elements are oriented cobordism classes〔Two compact oriented manifolds ''M'', ''N'' are oriented cobordant if there is a compact manifold with boundary such that the boundary is diffeomorphic to the disjoint union of ''M'' with the given orientation and ''N'' with the reversed orientation.〕 of manifolds, the multiplication is given by the Cartesian product of manifolds and the addition is given as the disjoint union of manifolds. The ring is graded by dimensions of manifolds and is denoted by :$\backslash Omega^\_$ * = \oplus_0^\infty \Omega^_n where $\backslash Omega^\_n$ consists of oriented cobordism classes of manifolds of dimension ''n''. One can also define an unoriented cobordism ring, denoted by $\backslash Omega^O\_$ *. If ''O'' is replaced ''U'', then one gets the complex cobordism ring, oriented or unoriented. In general, one writes $\backslash Omega^B\_$ * for the cobordism ring of manifolds with structure ''B''. A theorem of Thom〔http://math.northwestern.edu/~jnkf/classes/mflds/3thom.pdf〕 says: :$\backslash Omega^O\_n\; =\; \backslash pi\_(MO)$ where ''MO'' is the Thom spectrum. == Notes == 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「Cobordism ring」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.