{"paper":{"title":"Extension of isotopies in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GN","authors_text":"E. D. Tymchatyn, L. C. Hoehn, L. G. Oversteegen","submitted_at":"2018-08-16T17:45:40Z","abstract_excerpt":"Let $A$ be any plane set. It is known that a holomorphic motion $h: A \\times \\mathbb{D} \\to \\mathbb{C}$ always extends to a holomorphic motion of the entire plane. It was recently shown that any isotopy $h: X \\times [0,1] \\to \\mathbb{C}$, starting at the identity, of a plane continuum $X$ also extends to an isotopy of the entire plane. Easy examples show that this result does not generalize to all plane compacta. In this paper we will provide a characterization of isotopies of uniformly perfect plane compacta $X$ which extend to an isotopy of the entire plane. Using this characterization, we p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05601","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"}