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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 Elliptic complex ： ウィキペディア英語版 Elliptic complex In mathematics, in particular in partial differential equations and differential geometry, an elliptic complex generalizes the notion of an elliptic operator to sequences. Elliptic complexes isolate those features common to the de Rham complex and the Dolbeault complex which are essential for performing Hodge theory. They also arise in connection with the Atiyah-Singer index theorem and Atiyah-Bott fixed point theorem. ==Definition== If ''E''0, ''E''1, ..., ''E''''k'' are vector bundles on a smooth manifold ''M'' (usually taken to be compact), then a differential complex is a sequence :$\backslash Gamma(E\_0)\; \backslash stackrel\; \backslash Gamma(E\_1)\; \backslash stackrel\; \backslash ldots\; \backslash stackrel\; \backslash Gamma(E\_k)$ of differential operators between the sheaves of sections of the ''E''''i'' such that ''P''''i''+1 o ''P''''i''=0. A differential complex is elliptic if the sequence of symbols :$0\; \backslash rightarrow\; \backslash pi^$ *E_0 \stackrel \pi^ *E_1 \stackrel \ldots \stackrel \pi^ *E_k \rightarrow 0 is exact outside of the zero section. Here π is the projection of the cotangent bundle ''T *M'' to ''M'', and π * is the pullback of a vector bundle. 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「Elliptic complex」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.