{"paper":{"title":"Surgery on postcritically finite rational maps by blowing up an arc","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Kelvin Pilgrim, Tan Lei","submitted_at":"1995-12-18T00:00:00Z","abstract_excerpt":"Using Thurston's characterization of postcritically finite rational functions as branched coverings of the sphere to itself, we give a new method of constructing new conformal dynamical systems out of old ones. Let $f(z)$ be a rational map and suppose that the postcritical set $P(f)$ is finite. Let $\\alpha$ be an embedded closed arc in the sphere and suppose that $f|{\\alpha}$ is a homeomorphism. Define a branched covering $g$ as follows. Cut the sphere open along $\\alpha$. Glue in a closed disc $D$. Map $S^{2} - \\Int (D)$ via $f$ and $\\Int (D)$ by a homeomorphism to the complement of $f(\\alpha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9512221","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"}