Finite-volume hyperbolic 3-manifolds are almost determined by their finite quotient groups

Yi Liu

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arXiv · 2011.09412

Finite-volume hyperbolic 3-manifolds are almost determined by their finite quotient groups

Yi Liu

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Abstract

For any orientable finite-volume hyperbolic 3-manifold, this paper proves that the profinite isomorphism type of the fundamental group uniquely determines the isomorphism type of the first integral cohomology, as marked with the Thurston norm and the fibered classes; moreover, up to finite ambiguity, the profinite isomorphism type determines the isomorphism type of the fundamental group, among the class of finitely generated 3-manifold groups.

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Yi Liu. 2020-11-18. Finite-volume hyperbolic 3-manifolds are almost determined by their finite quotient groups. https://arxiv.org/abs/2011.09412

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