Epimorphisms of 3-manifold groups

Epimorphisms of 3-manifold groups

Abstract Let f:M→N be a proper map between two aspherical compact orientable 3-manifolds with empty or toroidal boundary. We assume that N is not a closed graph manifold. Suppose that f induces an epimorphism on fundamental groups. We show that f is homotopic to a homeomorphism if one of the followi...

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Veröffentlicht in:Quarterly journal of mathematics 2018-09, Vol.69 (3), p.931-942
Hauptverfasser: Boileau, Michel, Friedl, Stefan
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Sprache:eng
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Geometric Topology
Mathematics
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container_title Quarterly journal of mathematics
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creator Boileau, Michel
Friedl, Stefan
description Abstract Let f:M→N be a proper map between two aspherical compact orientable 3-manifolds with empty or toroidal boundary. We assume that N is not a closed graph manifold. Suppose that f induces an epimorphism on fundamental groups. We show that f is homotopic to a homeomorphism if one of the following holds: either for any finite-index subgroup Γ of π1(N) the ranks of Γ and of f⁎−1(Γ) agree, or for any finite cover N˜ of N the Heegaard genus of N˜ and the Heegaard genus of the pull-back cover M˜ agree.
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Mathematics
title Epimorphisms of 3-manifold groups
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