Work

Ascending Chains in 3-Manifold and Relatively Hyperbolic Groups

Year: 2026

Type: preprint

Abstract: We prove that any ascending chain of bounded rank subgroups in the fundamental group of a compact $3$-manifold stabilizes. We use geometrization to reduce the proof to fundamental groups of complete, finite-volume hyperbolic $3$-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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2603.27447

Authors: Bering, Edgar A., Heikamp, Jakob, Kohav, Jack, Lazarovich, Nir, Munro, Zachary

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Postdoctoral Fellowship: MSPRF: Cubulation and Combinatorial Nonpositive Curvature, LEAPS-MPS: Commensurations and Automorphisms of Free Groups via Topological Models

OpenAlex ID: W7147562778

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