{"paper":{"title":"Elliptic actions on Teichmuller space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Matthew Gentry Durham","submitted_at":"2014-12-30T04:04:52Z","abstract_excerpt":"Let $S$ be an oriented surface of finite type, $\\mathcal{MCG}(S)$ its mapping class group, and $\\mathcal{T}(S)$ its Teichm\\\"uller space with the Teichm\\\"uller metric. Let $H \\leq \\mathcal{MCG}(S)$ be a finite subgroup and consider the subset of $\\mathcal{T}(S)$ fixed by $H$, $\\mathrm{Fix}(H) \\subset \\mathcal{T}(S)$. For any $R>0$, we prove that the set of points whose $H$-orbits have diameter bounded by $R$, $\\mathrm{Fix}_R^T(H)$, lives in a bounded neighborhood of $\\mathrm{Fix}(H)$. As an application, we show that the orbit of any point $X \\in \\mathcal{T}(S)$ under the action of a finite orde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8559","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"}