{"paper":{"title":"Polishability of some groups of interval and circle diffeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Michael P. Cohen","submitted_at":"2017-09-13T20:00:45Z","abstract_excerpt":"Let $M=I$ or $M=\\mathbb{S}^1$ and let $k\\geq 1$. We exhibit a new infinite class of Polish groups by showing that each group $\\mathop{\\rm Diff}_+^{k+AC}(M)$, consisting of those $C^k$ diffeomorphisms whose $k$-th derivative is absolutely continuous, admits a natural Polish group topology which refines the subspace topology inherited from $\\mathop{\\rm Diff}_+^k(M)$. By contrast, the group $\\mathop{\\rm Diff}_+^{1+BV}(M)$, consisting of $C^1$ diffeomorphisms whose derivative has bounded variation, admits no Polish group topology whatsoever."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04523","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"}