{"paper":{"title":"A zoo of diffeomorphism groups on $\\mathbb R^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.FA","authors_text":"David Mumford, Peter W. Michor","submitted_at":"2012-11-24T20:37:18Z","abstract_excerpt":"We consider the groups $\\operatorname{Diff}_{\\mathcal B}(\\mathbb R^n)$, $\\operatorname{Diff}_{H^\\infty}(\\mathbb R^n)$, and $\\operatorname{Diff}_{\\mathcal S}(\\mathbb R^n)$ of smooth diffeomorphisms on $\\mathbb R^n$ which differ from the identity by a function which is in either $\\mathcal B$ (bounded in all derivatives), $H^\\infty = \\bigcap_{k\\ge 0}H^k$, or $\\mathcal S$ (rapidly decreasing). We show that all these groups are smooth regular Lie groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5704","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":""},"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"}