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July 2015 Virtual homological torsion of closed hyperbolic 3-manifolds
Hongbin Sun
J. Differential Geom. 100(3): 547-583 (July 2015). DOI: 10.4310/jdg/1432842365

Abstract

In this paper, we will use Kahn and Markovic’s immersed almost totally geodesic surfaces to construct certain immersed $\pi_1$-injective $2$-complexes in closed hyperbolic $3$-manifolds. Such $2$-complexes are locally almost totally geodesic except along a $1$-dimensional subcomplex. By using Agol’s result that the fundamental groups of closed hyperbolic $3$-manifolds are vitually compact special, and other works on geometric group theory, we will show that any closed hyperbolic $3$-manifold virtually contains any prescribed subgroup in the homological torsion. More precisely, our main result is, for any finite abelian group $A$, and any closed hyperbolic $3$-manifold $M, M$ admits a finite cover $N$, such that $A$ is a direct summand of $\mathit{Tor}(H_1(N; \mathbb{Z}))$.

Citation

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Hongbin Sun. "Virtual homological torsion of closed hyperbolic 3-manifolds." J. Differential Geom. 100 (3) 547 - 583, July 2015. https://doi.org/10.4310/jdg/1432842365

Information

Published: July 2015
First available in Project Euclid: 28 May 2015

zbMATH: 1350.57030
MathSciNet: MR3352799
Digital Object Identifier: 10.4310/jdg/1432842365

Rights: Copyright © 2015 Lehigh University

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Vol.100 • No. 3 • July 2015
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