English

Local connectedness of boundaries for relatively hyperbolic groups

Group Theory 2024-05-01 v2 Geometric Topology

Abstract

Let (Γ,P)(\Gamma,\mathbb{P}) be a relatively hyperbolic group pair that is relatively one ended. Then the Bowditch boundary of (Γ,P)(\Gamma,\mathbb{P}) is locally connected. Bowditch previously established this conclusion under the additional assumption that all peripheral subgroups are finitely presented, either one or two ended, and contain no infinite torsion subgroups. We remove these restrictions; we make no restriction on the cardinality of Γ\Gamma and no restriction on the peripheral subgroups PPP \in \mathbb{P}.

Keywords

Cite

@article{arxiv.2204.02463,
  title  = {Local connectedness of boundaries for relatively hyperbolic groups},
  author = {Ashani Dasgupta and G. Christopher Hruska},
  journal= {arXiv preprint arXiv:2204.02463},
  year   = {2024}
}

Comments

39 pages. Version 2 includes several clarifications in response to feedback from the referee. To appear in the Journal of Topology

R2 v1 2026-06-24T10:39:04.782Z