{"paper":{"title":"A trichotomy theorem for transformation groups of locally symmetric manifolds and topological rigidity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexander Lubotzky, Shmuel Weinberger, Sylvain Cappell","submitted_at":"2016-01-03T08:51:43Z","abstract_excerpt":"Let $M$ be a locally symmetric irreducible closed manifold of dimension $\\ge 3$. A result of Borel [Bo] combined with Mostow rigidity imply that there exists a finite group $G = G(M)$ such that any finite subgroup of $\\text{Homeo}^+(M)$ is isomorphic to a subgroup of $G$. Borel [Bo] asked if there exist $M$'s with $G(M)$ trivial and if the number of conjugacy classes of finite subgroups of $\\text{Homeo}^+(M)$ is finite. We answer both questions: (1) For every finite group $G$ there exist $M$'s with $G(M) = G$, and (2) the number of maximal subgroups of $\\text{Homeo}^+(M)$ can be either one, co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00262","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":""},"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"}