{"paper":{"title":"Automorphisms of the sphere complex of an infinite graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Brian Udall, George Shaji, Michael C. Kopreski, Rebecca Rechkin, Thomas Hill","submitted_at":"2024-10-09T04:09:20Z","abstract_excerpt":"For a locally finite, connected graph $\\Gamma$, let $\\operatorname{Map}(\\Gamma)$ denote the group of proper homotopy equivalences of $\\Gamma$ up to proper homotopy. Excluding sporadic cases, we show $\\operatorname{Aut}(S(M_\\Gamma)) \\cong \\operatorname{Map}(\\Gamma)$, where $\\mathcal{S}(M_\\Gamma)$ is the sphere complex of the doubled handlebody $M_\\Gamma$ associated to $\\Gamma$. We also construct an exhaustion of $S(M_\\Gamma)$ by finite strongly rigid sets when $\\Gamma$ has finite rank and finitely many rays, and an appropriate generalization otherwise."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.06531","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/2410.06531/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"}