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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 Pseudoisotopy theorem ： ウィキペディア英語版 Pseudoisotopy theorem In mathematics, the pseudoisotopy theorem is a theorem of Jean Cerf's〔(French mathematician, born 1928 )〕 which refers to the connectivity of a group of diffeomorphisms of a manifold. == Statement == Given a differentiable manifold ''M'' (with or without boundary), a pseudo-isotopy diffeomorphism of ''M'' is a diffeomorphism of ''M'' × () which restricts to the identity on $M\; \backslash times\; \backslash \; \backslash cup\; \backslash partial\; M\; \backslash times\; ()$. Given $f\; :\; M\; \backslash times\; ()\; \backslash to\; M\; \backslash times\; ()$ a pseudo-isotopy diffeomorphism, its restriction to $M\; \backslash times\; \backslash$ is a diffeomorphism $g$ of ''M''. We say ''g'' is ''pseudo-isotopic to the identity''. One should think of a pseudo-isotopy as something that is almost an isotopy—the obstruction to ''ƒ'' being an isotopy of ''g'' to the identity is whether or not ''ƒ'' preserves the level-sets $M\; \backslash times\; \backslash$ for $t\; \backslash in\; ()$. Cerf's theorem states that, provided ''M'' is simply-connected and dim(''M'') ≥ 5, the group of pseudo-isotopy diffeomorphisms of ''M'' is connected. Equivalently, a diffeomorphism of ''M'' is isotopic to the identity if and only if it is pseudo-isotopic to the identity. 〔 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「Pseudoisotopy 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.