{"paper":{"title":"Conjugacy Distinguished Cosets in Hyperbolic $3$-Manifold Groups","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"David Futer, Emily Hamilton, Neil R Hoffman","submitted_at":"2026-06-24T01:48:17Z","abstract_excerpt":"A subset $S$ of a group $G$ is \\emph{conjugacy distinguished} if the union of all conjugates of $S$ is closed in the profinite topology on $G$. We prove that if $M = \\mathbb{H}^3/\\Gamma$ is a hyperbolic $3$-manifold of finite volume, $g \\in \\Gamma$, and $H$ is an abelian subgroup of $\\Gamma$, then the coset $gH$ is conjugacy distinguished in $\\Gamma$. A subset $S \\subset G$ is \\emph{conjugacy distinguished from a class of subgroups} if, for every $K$ in the class that is disjoint from the union of conjugates of $S$, there exists a homomorphism $\\varphi \\colon G \\rightarrow F$, where $F$ is a f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25289","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.25289/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}