Ascending Chains in 3-Manifold and Relatively Hyperbolic Groups
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915897349767168 |
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| author | Bering IV, Edgar A. Heikamp, Jakob Kohav, Jack Lazarovich, Nir Munro, Zachary |
| author_facet | Bering IV, Edgar A. Heikamp, Jakob Kohav, Jack Lazarovich, Nir Munro, Zachary |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27447 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ascending Chains in 3-Manifold and Relatively Hyperbolic Groups Bering IV, Edgar A. Heikamp, Jakob Kohav, Jack Lazarovich, Nir Munro, Zachary Group Theory Geometric Topology 20F65, 20E08, 57K30 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. |
| title | Ascending Chains in 3-Manifold and Relatively Hyperbolic Groups |
| topic | Group Theory Geometric Topology 20F65, 20E08, 57K30 |
| url | https://arxiv.org/abs/2603.27447 |