{"paper":{"title":"Simplicity of the contactomorphism group of finite regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GT"],"primary_cat":"math.SG","authors_text":"Yong-Geun Oh","submitted_at":"2024-03-27T05:28:05Z","abstract_excerpt":"For a given coorientable contact manifold $(M^{2n+1},\\xi)$, we consider the group $ \\operatorname{Cont}_c^{(r,\\delta)}(M,\\alpha)$ consisting of $C^{r,\\delta}$ contactomorphisms with compact support which is equipped with $C^{r,\\delta}$-topology of H\\\"older regularity $(r,\\delta)$ for $r \\geq 1$ and $0 <\\delta \\leq 1$. We prove that for all H\\\"older class exponents with $r > n + 2$ or $r = n+1, \\, \\frac12 < \\delta \\leq 1$ (resp. $r < n+1$ or $r = n+1$ and $ 0< \\delta <\\frac12$), the group is a perfect (and so a simple) group. In particular, $\\operatorname{Cont}_c^r(M,\\xi)$ is simple for all int"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.18261","kind":"arxiv","version":2},"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/2403.18261/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"}