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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 De Rham invariant ： ウィキペディア英語版 De Rham invariant In geometric topology, the de Rham invariant is a mod 2 invariant of a (4''k''+1)-dimensional manifold, that is, an element of $\backslash mathbf/2$ – either 0 or 1. It can be thought of as the simply-connected ''symmetric'' L-group $L^,$ and thus analogous to the other invariants from L-theory: the signature, a 4''k''-dimensional invariant (either symmetric or quadratic, $L^\; \backslash cong\; L\_$), and the Kervaire invariant, a (4''k''+2)-dimensional ''quadratic'' invariant $L\_.$ It is named for Swiss mathematician Georges de Rham, and used in surgery theory.〔Morgan & Sullivan, ''The transversality characteristic class and linking cycles in surgery theory,'' 1974〕〔John W. Morgan, ''(A product formula for surgery obstructions ),'' 1978〕 == Definition == The de Rham invariant of a (4''k''+1)-dimensional manifold can be defined in various equivalent ways: * the rank of the 2-torsion in $H\_(M),$ as an integer mod 2; * the Stiefel–Whitney number $w\_2w\_$; * the (squared) Wu number, $v\_Sq^1v\_,$ where $v\_\; \backslash in\; H^(M;Z\_2)$ is the Wu class of the normal bundle of $M$ and $Sq^1$ is the Steenrod square ; formally, as with all characteristic numbers, this is evaluated on the fundamental class: $(v\_Sq^1v\_,())$; * in terms of a semicharacteristic. 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「De Rham invariant」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.