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Dehn surgery

Dehn 割补术

本站译名 几何拓扑与低维拓扑 义项编号TS-2167

中文别名
Dehn 嵌块术

外文出处

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Chromatic Homotopy Theory Jacob Lurie

《Chromatic Homotopy Theory》 · 第 305、356 页 · Section 10.1.1,Definition 10.1.1;Section 11.3.3(filling 与 surgery 的定义)

Let \(M\) be a 3-manifold and \(T\subset\partial M\) be a boundary torus component. A Dehn filling of \(M\) along \(T\) is the operation of gluing a solid torus \(D\times S^1\) to \(M\) via a diffeomorphism \(\phi:\partial D\times S^1\longrightarrow T\). […] Let \(L\subset M\) be a link with \(k\) components in an orientable 3-manifold \(M\). A Dehn surgery on \(L\) is a Dehn filling of the complement of \(L\). That is, it is a two-step operation that consists of: (1) (drilling) the removal of small open tubular neighbourhoods of \(L\), that creates new boundary tori \(T_1,\ldots,T_k\); (2) (filling) a Dehn filling of the new boundary tori \(T_1,\ldots,T_k\).

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