Epimorphisms of 3-manifold groups

2016/02/22 by Boileau, Michel, Friedl, Stefan
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1602.06779

Abstract

Let f\colon 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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