{"paper":{"title":"Almost fixed points of finite group actions on manifolds without odd cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.GT"],"primary_cat":"math.DG","authors_text":"Ignasi Mundet i Riera","submitted_at":"2018-05-07T15:43:44Z","abstract_excerpt":"If $X$ is a smooth manifold and ${\\mathcal{G}}$ is a subgroup of $Diff(X)$ we say that $(X,{\\mathcal{G}})$ has the almost fixed point property if there exists a number $C$ such that for any finite subgroup $G\\leq{\\mathcal{G}}$ there is some $x\\in X$ whose stabilizer $G_x\\leq G$ satisfies $[G:G_x]\\leq C$. We say that $X$ has no odd cohomology if its integral cohomology is torsion free and supported in even degrees. We prove that if $X$ is compact and possibly with boundary and has no odd cohomology then $(X,Diff(X))$ has the almost fixed point property. Combining this with a result of Petrie an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02582","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"}