翻訳と辞書 Words near each other ・ ATIV Software ・ Ativin ・ Atiwa (Ghana parliament constituency) ・ Atiwa District ・ Atiyah ・ Atiyah Abd al-Rahman ・ Atiyah algebroid ・ Atiyah conjecture ・ Atiyah conjecture on configurations ・ Atiyah's Accidents, Compensation and the Law ・ Atiyah–Bott fixed-point theorem ・ Atiyah–Bott formula ・ Atiyah–Hirzebruch spectral sequence ・ Atiyah–Hitchin–Singer theorem ・ Atiyah–Jones conjecture ・ Atiyah–Segal completion theorem ・ Atiyah–Singer index theorem ・ Atiye ・ Atiye Sultan ・ Atiyeh, Khuzestan ・ Atiyya ibn Sa'd ・ Atiyyah Ellison ・ Atizoram ・ Atiśa ・ Atje Keulen-Deelstra ・ Atjeh Tram ・ Atjeh United F.C. ・ Atjeh-class cruiser ・ ATK ・ ATK motorcycles 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 Atiyah–Segal completion theorem ： ウィキペディア英語版 Atiyah–Segal completion theorem The Atiyah–Segal completion theorem is a theorem in mathematics about equivariant K-theory in homotopy theory. Let ''G'' be a compact Lie group and let ''X'' be a ''G''-CW-complex. The theorem then states that the projection map :$\backslash pi\backslash colon\; X\backslash times\; EG\backslash to\; X$ induces an isomorphism of prorings :$\backslash pi^$ *\colon K_G^ *(X)\hat\to K_G^ *(X\times EG). Here, the induced map has as domain the completion of the ''G''-equivariant K-theory of ''X'' with respect to ''I'', where ''I'' denotes the augmentation ideal of the representation ring of ''G''. In the special case of ''X'' a point, the theorem specializes to give an isomorphism $K^$ *(BG)\cong R(G)\hat between the K-theory of the classifying space of ''G'' and the completion of the representation ring. The theorem can be interpreted as giving a comparison between the geometrical process of completing a ''G''-space by making the action free and the algebraic process of completing with respect to an ideal. The theorem was first proved for finite groups by Michael Atiyah in 1961, and a proof of the general case was published by Atiyah together with Graeme Segal in 1969. Different proofs have since appeared generalizing the theorem to completion with respect to families of subgroups. The corresponding statement for algebraic K-theory was proven by Merkujev, holding in the case that the group is algebraic over the complex numbers. ==See also== *Segal conjecture 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「Atiyah–Segal completion theorem」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.