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 -manifold stabilizes. We use geometrization to reduce the proof to fundamental groups of complete, finite-volume hyperbolic -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.
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