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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 Dehn surgery ： ウィキペディア英語版 Dehn surgery In topology, a branch of mathematics, a Dehn surgery, named after Max Dehn, is a construction used to modify 3-manifolds. The process takes as input a 3-manifold together with a link. Dehn surgery can be thought of as a two-stage process: drilling and Dehn filling. ==Definitions== * Given a 3-manifold $M$ and a link $L\; \backslash subset\; M$, ''$M$ drilled along $L$'' is obtained by removing an open tubular neighborhood of $L$ from $M$. ''$M$ drilled along $L$'' is also known as the link complement, since if one removed the corresponding closed tubular neighborhood from $M$ one obtains a manifold diffeomorphic to $M\; \backslash setminus\; L$. * Given a 3-manifold with torus boundary components, we may glue in a solid torus by a homeomorphism (resp. diffeomorphism) of its boundary to the torus boundary component $T$ of the original 3-manifold. There are many inequivalent ways of doing this, in general. This process is called Dehn filling. * Dehn surgery on a 3-manifold containing a link consists of drilling out a tubular neighbourhood of the link together with Dehn filling on all the components of the boundary corresponding to the link. We can pick two oriented simple closed curves ''m'' and ''ℓ'' on the boundary torus of the 3-manifold that generate the fundamental group of the torus. This gives any simple closed curve $\backslash gamma$ on that torus two coordinates ''p'' and ''q'', each coordinate corresponding to the algebraic intersection of the curve with ''m'' and ''ℓ'' respectively. These coordinates only depend on the homotopy class of $\backslash gamma$. We can specify a homeomorphism of the boundary of a solid torus to ''T'' by having the meridian curve of the solid torus map to a curve homotopic to $\backslash gamma$. As long as the meridian maps to the surgery slope $()$, the resulting Dehn surgery will yield a 3-manifold that will not depend on the specific gluing (up to homeomorphism). The ratio ''p''/''q'' is called the surgery coefficient. In the case of links in the 3-sphere or more generally an oriented homology sphere, there is a canonical choice of the meridians and longitudes of ''T''. The longitude is chosen so that it is null-homologous in the knot complement—equivalently, if it is the boundary of a Seifert surface. The meridian is the curve that bounds a disc in the tubular neighbourhood of the link. When the ratios ''p''/''q'' are all integers, the surgery is called an ''integral surgery''. Such surgeries are closely related to handlebodies, cobordism and Morse functions. 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「Dehn surgery」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.