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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 Kirwan map ： ウィキペディア英語版 Kirwan map In differential geometry, the Kirwan map, introduced by British mathematician Frances Kirwan, is the homomorphism :$H^$ *_G(M) \to H^ *(M /\!/_p G) where *''M'' is a Hamiltonian G-space; i.e., a symplectic manifold acted by a Lie group ''G'' with a moment map $\backslash mu:\; M\; \backslash to\; ^$ *. *$H^$ *_G(M) is the equivariant cohomology ring of ''M''; i.e.. the cohomology ring of the homotopy quotient $EG\; \backslash times\_G\; M$ of ''M'' by ''G''. *$M\; /\backslash !/\_p\; G\; =\; \backslash mu^(p)/G$ is the symplectic quotient of ''M'' by ''G'' at a regular central value $p\; \backslash in\; Z(^$ *) of $\backslash mu$. It is defined as the map of equivariant cohomology induced by the inclusion $\backslash mu^(p)\; \backslash hookrightarrow\; M$ followed by the canonical isomorphism $H\_G^$ *(\mu^(p)) = H^ *(M /\!/_p G). A theorem of Kirwan says that if ''M'' is compact, then the map is surjective in rational coefficients. The analogous result holds between the K-theory of the symplectic quotient and the equivariant topological K-theory of ''M''.〔M. Harada, G. Landweber. Surjectivity for Hamiltonian G-spaces in K-theory. Trans. Amer. Math. Soc. 359 (2007), 6001--6025.〕 == References == 〔 *F. C. Kirwan, Cohomology of Quotients in Complex and Algebraic Geometry, Mathematical Notes 31, Princeton University Press, Princeton N. J., 1984. 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「Kirwan map」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.