{"paper":{"title":"Which finite groups act smoothly on a given $4$-manifold?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.GT","math.SG"],"primary_cat":"math.DG","authors_text":"Carles S\\'aez-Calvo, Ignasi Mundet i Riera","submitted_at":"2019-01-14T10:31:32Z","abstract_excerpt":"We prove that for any closed smooth $4$-manifold $X$ there exists a constant $C$ with the property that each finite subgroup $G<Diff(X)$ has a subgroup $N$ which is abelian or nilpotent of class $2$, and which satisfies $[G:N]\\leq C$. We give sufficient conditions on $X$ for $Diff(X)$ to be Jordan, meaning that there exists a constant $C$ such that any finite subgroup $G<Diff(X)$ has an abelian subgroup $A$ satisfying $[G:A]\\leq C$. Some of these conditions are homotopical, such as having nonzero Euler characteristic or nonzero signature, others are geometric, such as the absence of embedded t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.04223","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"}