{"paper":{"title":"Finite rigid sets and homologically non-trivial spheres in the curve complex of a surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Joan Birman, Nathan Broaddus, William Menasco","submitted_at":"2013-11-29T17:52:24Z","abstract_excerpt":"Aramayona and Leininger have provided a \"finite rigid subset\" $\\mathfrak{X}(\\Sigma)$ of the curve complex $\\mathscr{C}(\\Sigma)$ of a surface $\\Sigma = \\Sigma^n_g$, characterized by the fact that any simplicial injection $\\mathfrak{X}(\\Sigma) \\to \\mathscr{C}(\\Sigma)$ is induced by a unique element of the mapping class group $\\mathrm{Mod}(\\Sigma)$. In this paper we prove that, in the case of the sphere with $n\\geq 5$ marked points, the reduced homology class of the finite rigid set of Aramayona and Leininger is a $\\mathrm{Mod}(\\Sigma)$-module generator for the reduced homology of the curve compl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7646","kind":"arxiv","version":3},"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"}