English

Rank and Nielsen equivalence in hyperbolic extensions

Geometric Topology 2018-12-21 v2 Group Theory

Abstract

In this note, we generalize a theorem of Juan Souto on rank and Nielsen equivalence in the fundamental group of a hyperbolic fibered 3-manifold to a large class of hyperbolic group extensions. This includes all hyperbolic extensions of surfaces groups as well as hyperbolic extensions of free groups by convex cocompact subgroups of Out(Fn)(F_n).

Keywords

Cite

@article{arxiv.1706.02368,
  title  = {Rank and Nielsen equivalence in hyperbolic extensions},
  author = {Spencer Dowdall and Samuel J. Taylor},
  journal= {arXiv preprint arXiv:1706.02368},
  year   = {2018}
}

Comments

v2: 10 pages. Minor updates to incorporate referee comments. Added counter-example demonstrating necessity of torsion free hypothesis. Final version; accepted for publication in the International Journal of Algebra and Computation (IJAC)