English

On a generalization of Cannon's conjecture for cubulated hyperbolic groups

Geometric Topology 2024-06-14 v1 Group Theory

Abstract

We show that cubulated hyperbolic groups with spherical boundary of dimension 3 or at least 5 are virtually fundamental groups of closed, orientable, aspherical manifolds, provided that there are sufficiently many quasi-convex, codimension-1 subgroups whose limit sets are locally flat subspheres. The proof is based on ideas used by Markovic in his work on Cannon's conjecture for cubulated hyperbolic groups with 2-sphere boundary.

Keywords

Cite

@article{arxiv.2406.08779,
  title  = {On a generalization of Cannon's conjecture for cubulated hyperbolic groups},
  author = {Corey Bregman and Merlin Incerti-Medici},
  journal= {arXiv preprint arXiv:2406.08779},
  year   = {2024}
}

Comments

26 pages, 1 figure, 1 appendix. Comments welcome