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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 Equivariant index theorem ： ウィキペディア英語版 Equivariant index theorem In differential geometry, the equivariant index theorem, of which there are several variants, computes the (graded) trace of an element of a compact Lie group acting in given setting in terms of the integral over the fixed points of the element. If the element is neutral, then the theorem reduces to the usual index theorem. The classical formula such as the Atiyah–Bott formula is a special case of the theorem. == Statement == Let $\backslash pi:\; E\; \backslash to\; M$ be a clifford module bundle. Assume a compact Lie group ''G'' acts on both ''E'' and ''M'' so that $\backslash pi$ is equivariant. Let ''E'' be given a connection that is compatible with the action of ''G''. Finally, let ''D'' be a Dirac operator on ''E'' associated to the given data. In particular, ''D'' commutes with ''G'' and thus the kernel of ''D'' is a finite-dimensional representation of ''G''. The equivariant index of ''E'' is a virtual character given by taking the supertrace: :$\backslash operatorname(g\backslash mid\backslash ker\; D)\; =\; \backslash operatorname(g\backslash mid\backslash ker\; D^+)\; -\; \backslash operatorname(g\backslash mid\backslash ker\; D^-).$ 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「Equivariant index 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.