{"paper":{"title":"On Thurston's pullback map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Adam Epstein, Kevin Pilgrim, Sarah Koch, Xavier Buff","submitted_at":"2011-05-09T19:47:24Z","abstract_excerpt":"Let f: P^1 \\to P^1 be a rational map with finite postcritical set P_f. Thurston showed that f induces a holomorphic map \\sigma_f of the Teichmueller space T modelled on P_f to itself fixing the basepoint corresponding to the identity map (P^1, P_f) \\to (P^1, P_f). We give explicit examples of such maps f showing that the following cases may occur: (1) the basepoint is an attracting fixed point, the image of \\sigma_f is open and dense, and the map \\sigma_f is a covering map onto its image; (2) the basepoint is a superattracting fixed point, \\sigma is surjective, and \\sigma is a ramified Galois "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1763","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"}