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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 Symplectic cut ： ウィキペディア英語版 Symplectic cut In mathematics, specifically in symplectic geometry, the symplectic cut is a geometric modification on symplectic manifolds. Its effect is to decompose a given manifold into two pieces. There is an inverse operation, the symplectic sum, that glues two manifolds together into one. The symplectic cut can also be viewed as a generalization of symplectic blow up. The cut was introduced in 1995 by Eugene Lerman, who used it to study the symplectic quotient and other operations on manifolds. == Topological description == Let $(X,\; \backslash omega)$ be any symplectic manifold and :$\backslash mu\; :\; X\; \backslash to\; \backslash mathbb$ a Hamiltonian on $X$. Let $\backslash epsilon$ be any regular value of $\backslash mu$, so that the level set $\backslash mu^(\backslash epsilon)$ is a smooth manifold. Assume furthermore that $\backslash mu^(\backslash epsilon)$ is fibered in circles, each of which is an integral curve of the induced Hamiltonian vector field. Under these assumptions, $\backslash mu^((\backslash infty))$ is a manifold with boundary $\backslash mu^(\backslash epsilon)$, and one can form a manifold :$\backslash overline\_$ by collapsing each circle fiber to a point. In other words, $\backslash overline\_$ is $X$ with the subset $\backslash mu^((-\backslash infty,\; \backslash epsilon))$ removed and the boundary collapsed along each circle fiber. The quotient of the boundary is a submanifold of $\backslash overline\_$ of codimension two, denoted $V$. Similarly, one may form from $\backslash mu^((-\backslash infty,\; \backslash epsilon\; ))$ a manifold $\backslash overline\_$, which also contains a copy of $V$. The symplectic cut is the pair of manifolds $\backslash overline\_$ and $\backslash overline\_$. Sometimes it is useful to view the two halves of the symplectic cut as being joined along their shared submanifold $V$ to produce a singular space :$\backslash overline\_\; \backslash cup\_V\; \backslash overline\_.$ For example, this singular space is the central fiber in the symplectic sum regarded as a deformation. 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「Symplectic cut」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.