{"paper":{"title":"A disconnected deformation space of rational maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Eriko Hironaka, Sarah Koch","submitted_at":"2016-02-24T03:19:14Z","abstract_excerpt":"Let $f:(\\mathbb{P}^1,P)\\to(\\mathbb{P}^1,P)$ be a postcritically finite rational map with postcritical set $P$. William Thurston showed that $f$ induces a holomorphic pullback map $\\sigma_f:\\mathcal{T}_P\\to\\mathcal{T}_P$ on the Teichm\\\"uller space ${\\mathcal T}_P:=\\mathrm{Teich}(\\mathbb{P}^1,P)$. If $f$ is not a flexible Latt\\`es map, Thurston proved that $\\sigma_f$ has a unique fixed point. In his PhD thesis, Adam Epstein generalized Thurston's ideas and defined a deformation space associated to a rational map $f:(\\mathbb{P}^1,A)\\to (\\mathbb{P}^1,B)$ where $A \\subseteq B$, allowing for maps $f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07378","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"}