{"paper":{"title":"On Fenchel-Nielsen coordinates on Teichm\\\"uller spaces of surfaces of infinite type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Athanase Papadopoulos (IRMA, Daniele Alessandrini (IRMA), Lixin Liu, MPI), Weixu Su, Zongliang Sun","submitted_at":"2010-03-04T07:38:53Z","abstract_excerpt":"We introduce Fenchel-Nielsen coordinates on Teicm\\\"uller spaces of surfaces of infinite type. The definition is relative to a given pair of pants decomposition of the surface. We start by establishing conditions under which any pair of pants decomposition on a hyperbolic surface of infinite type can be turned into a geometric decomposition, that is, a decomposition into hyperbolic pairs of pants. This is expressed in terms of a condition we introduce and which we call Nielsen convexity. This condition is related to Nielsen cores of Fuchsian groups. We use this to define the Fenchel-Nielsen Tei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.0980","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"}