English

Ascending Chains in 3-Manifold and Relatively Hyperbolic Groups

Group Theory 2026-03-31 v1 Geometric Topology

Abstract

We prove that any ascending chain of bounded rank subgroups in the fundamental group of a compact 33-manifold stabilizes. We use geometrization to reduce the proof to fundamental groups of complete, finite-volume hyperbolic 33-manifolds. To handle this case, we prove the following: In a toral relatively hyperbolic group, any ascending chain of bounded rank, locally relatively quasiconvex subgroups stabilizes. We note this theorem is new even for bounded rank, locally quasiconvex chains in hyperbolic groups.

Keywords

Cite

@article{arxiv.2603.27447,
  title  = {Ascending Chains in 3-Manifold and Relatively Hyperbolic Groups},
  author = {Edgar A. Bering and Jakob Heikamp and Jack Kohav and Nir Lazarovich and Zachary Munro},
  journal= {arXiv preprint arXiv:2603.27447},
  year   = {2026}
}

Comments

28 pages, 1 figure

R2 v1 2026-07-01T11:42:33.506Z