{"paper":{"title":"Finite group actions on 4-manifolds with nonzero Euler characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DG","authors_text":"Ignasi Mundet i Riera","submitted_at":"2013-12-11T12:59:45Z","abstract_excerpt":"We prove that if $X$ is a compact, oriented, connected $4$-dimensional smooth manifold, possibly with boundary, satisfying $\\chi(X)\\neq 0$, then there exists an integer $C\\geq 1$ such that any finite group $G$ acting smoothly and effectively on $X$ has an abelian subgroup $A$ satisfying $[G:A]\\leq C$, $\\chi(X^A)=\\chi(X)$, and $A$ can be generated by at most $2$ elements. Furthermore, if $\\chi(X)<0$ then $A$ is cyclic. This proves, for any such $X$, a conjecture of Ghys. We also prove an analogous result for manifolds of arbitrary dimension and non-vanishing Euler characteristic, but restricted"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3149","kind":"arxiv","version":3},"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"}