{"paper":{"title":"On the automorphisms group of the asymptotic pants complex of an infinite surface of genus zero","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Louis Funar, Maxime Nguyen","submitted_at":"2013-08-28T12:30:44Z","abstract_excerpt":"The braided Thompson group $\\mathcal B$ is an asymptotic mapping class group of a sphere punctured along the standard Cantor set, endowed with a rigid structure. Inspired from the case of finite type surfaces we consider a Hatcher-Thurston cell complex whose vertices are asymptotically trivial pants decompositions. We prove that the automorphism group $\\hat{\\mathcal B^{\\frac{1}{2}}}$ of this complex is also an asymptotic mapping class group in a weaker sense. Moreover $\\hat{\\mathcal B^{\\frac{1}{2}}}$ is obtained by $\\mathcal B$ by first adding new elements called half-twists and further comple"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6143","kind":"arxiv","version":2},"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"}