Virtual Homological Torsion of Closed Hyperbolic 3-manifolds
Virtual Homological Torsion of Closed Hyperbolic 3-manifolds
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DOI：
10.4310/jdg/1432842365
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发表时间：
2013-09
期刊：
影响因子：
--
通讯作者：
Hongbin Sun
中科院分区：
文献类型：
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作者：
Hongbin Sun
In this paper, we will use Kahn-Markovic's almost totally geodesic surfaces to construct certain $\pi_1$-injective 2-complexes in closed hyperbolic 3-manifolds. Such 2-complexes are locally almost totally geodesic except along a 1-dimensional subcomplex. Using Agol and Wise's result that fundamental groups of hyperbolic 3-manifolds are LERF and quasi-convex subgroups are virtual retract, we will show that closed hyperbolic 3-manifolds virtually contain any prescribed homological torsion: For any finite abelian group $A$, and any closed hyperbolic 3-manifold $M$, there exists a finite cover $N$ of $M$, such that $A$ is a direct summand of $Tor(H_1(N;\mathbb{Z}))$.
