翻訳と辞書 Words near each other ・ Complex structured finance transactions ・ Complex system ・ Complex systems ・ Complex Systems (journal) ・ Complex systems biology ・ Complex text layout ・ Complex torus ・ Complex training ・ Complex variables ・ Complex vector bundle ・ Complex vertebral malformation ・ Complex volcano ・ Complex Volume 1 ・ Complex wavelet transform ・ Complex-analytic variety ・ Complex-oriented cohomology theory ・ Complex-toothed flying squirrel ・ Complex-valued function ・ Complexa ・ Complexe Al Amal ・ Complexe de Kawani ・ Complexe Desjardins ・ Complexe Guy-Favreau ・ Complexe Les Ailes ・ Complexe Maisonneuve ・ Complexe OCP ・ Complexe sonore ・ Complexe sportif Claude-Robillard ・ Complexe Sportif d'El Alia ・ Complexe Sportif René Tys Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Complex-oriented cohomology theory ： ウィキペディア英語版 Complex-oriented cohomology theory In algebraic topology, a complex-orientable cohomology theory is a multiplicative cohomology theory ''E'' such that the restriction map $E^2(\backslash mathbb\backslash mathbf^\backslash infty)\; \backslash to\; E^2(\backslash mathbb\backslash mathbf^1)$ is surjective. An element of $E^2(\backslash mathbb\backslash mathbf^\backslash infty)$ that restricts to the canonical generator of the reduced theory $\backslash widetilde^2(\backslash mathbb\backslash mathbf^1)$ is called a complex orientation. The notion is central to Quillen's work relating cohomology to formal group laws. If $\backslash pi\_3\; E\; =\; \backslash pi\_5\; E\; =\; \backslash cdots$, then ''E'' is complex-orientable. Examples: *An ordinary cohomology with any coefficient ring ''R'' is complex orientable, as $\backslash operatorname^2(\backslash mathbb\backslash mathbf^\backslash infty;\; R)\; \backslash simeq\; \backslash operatorname^2(\backslash mathbb\backslash mathbf^1;R)$. *A complex ''K''-theory, denoted by ''K'', is complex-orientable, as $\backslash pi\_3\; K\; =\; \backslash pi\_5\; K\; =\; \backslash cdots\; =\; 0$ (Bott periodicity theorem) *Complex cobordism, whose spectrum is denoted by MU, is complex-orientable. A complex orientation, call it ''t'', gives rise to a formal group law as follows: let ''m'' be the multiplication :$\backslash mathbb\backslash mathbf^\backslash infty\; \backslash times\; \backslash mathbb\backslash mathbf^\backslash infty\; \backslash to\; \backslash mathbb\backslash mathbf^\backslash infty,\; ((),\; ())\; \backslash mapsto\; ()$ where $()$ denotes a line passing through ''x'' in the underlying vector space $\backslash mathbb()$ of $\backslash mathbb\backslash mathbf^\backslash infty$. Viewing :$E^$ *(\mathbb\mathbf^\infty) = \varprojlim E^ *(\mathbb\mathbf^n) = \varprojlim R()/(t^) = R, \quad R =\pi_ * E = \oplus \pi_ E, let $f\; =\; m^$ *(t) be the pullback of ''t'' along ''m''. It lives in :$E^$ *(\mathbb\mathbf^\infty \times \mathbb\mathbf^\infty) = \varprojlim E^ *(\mathbb\mathbf^n \times \mathbb\mathbf^m) = \varprojlim R()/(x^,y^) = R and one can show it is a formal group law (e.g., satisfies associativity). == See also == *Chromatic homotopy theory 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「Complex-oriented cohomology theory」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.