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Seifert fibration

Seifert 纤维化

本站译名 几何拓扑与低维拓扑 义项编号TS-2190

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Chromatic Homotopy Theory Jacob Lurie

《Chromatic Homotopy Theory》 · 第 317–318 页 · Section 10.3.2,标准纤维环体的定义及 Definition 10.3.7

Let \((p,q)\) be two coprime integers with \(p>0\). A standard fibered solid torus with coefficients \((p,q)\) is the solid torus \(D\times[0,1]/\psi\) where \(\psi:D\times0\longrightarrow D\times1\) is a rotation of angle \(2\pi q/p\). The fibration into vertical segments \(\{\mathrm{pt}\}\times[0,1]\) extends to a fibration into circles of the solid torus. […] A Seifert fibration is a partition of a compact oriented 3-manifold \(N\) with (possibly empty) boundary into circles, such that every circle has a fibered neighbourhood diffeomorphic to a standard fibered solid torus.

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