Boileau, Michel and Friedl, Stefan (2018) EPIMORPHISMS OF 3-MANIFOLD GROUPS. QUARTERLY JOURNAL OF MATHEMATICS, 69 (3). pp. 931-942. ISSN 0033-5606, 1464-3847
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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 Gamma of pi(1)(N) the ranks of Gamma and of f(*)(-1) (Gamma) agree, or for any finite cover (N) over tilde of N the Heegaard genus of (N) over tilde and the Heegaard genus of the pull-back cover (M) over tilde agree.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | GRAPH MANIFOLDS; HEEGAARD-SPLITTINGS; HAKEN CONJECTURE; SURFACE BUNDLES; CYCLIC COVERS; RANK; RIGIDITY; GENUS; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Stefan Friedl |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 09 Jan 2020 07:44 |
| Last Modified: | 09 Jan 2020 07:44 |
| URI: | https://pred.uni-regensburg.de/id/eprint/13953 |
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