The panted cobordism groups of cusped hyperbolic 3-manifolds

Pub Date : 2022-07-12 DOI:10.1112/topo.12255

Hongbin Sun

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引用次数: 2

Abstract

For any oriented cusped hyperbolic 3-manifold $M$ , we study its $(R, ε)$ -panted cobordism group, which is the abelian group generated by $(R, ε)$ -good curves in $M$ modulo the oriented boundaries of $(R, ε)$ -good pants. In particular, we prove that for sufficiently small $ε > 0$ and sufficiently large $R > 0$ , some modified version of the $(R, ε)$ -panted cobordism group of $M$ is isomorphic to $H_{1} (SO (M); Z)$ .

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顶角双曲3-流形的共轭群

对于任意有向双曲3流形M$ M$，我们研究了它的(R， ε)$ (R，\epsilon)$ -共轭群，它是由M$ M$中的(R， ε)$ (R，\epsilon)$ -good曲线模取(R)$的有向边界所生成的阿贝尔群，ε)$ (R，\epsilon)$ -好裤子。特别地，我们证明了当ε >0$ \ ε >0$和足够大的R >0$ R>0$，是(R)的修改版本，M$ M$的ε)$ (R，\ ε)$ -共轭群同构于h1 (SO (M);$H_1(\text{SO}(M);\mathbb {Z})$。

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