{"paper":{"title":"A Curve Complex and Incompressible Surfaces in $S\\times \\mathbb{R}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ingrid Irmer","submitted_at":"2011-08-21T20:13:42Z","abstract_excerpt":"Various curve complexes with vertices representing multicurves on a surface $S$ have been defined, for example [3], [4] and [8]. The homology curve complex $\\mathcal{HC}(S,\\alpha)$ defined in [7] is one such complex, with vertices corresponding to multicurves in a nontrivial integral homology class $\\alpha$. Given two multicurves $m_1$ and $m_2$ corresponding to vertices in $\\mathcal{HC}(S,\\alpha)$, it was shown in [8] that a path in $\\mathcal{HC}(S,\\alpha)$ connecting these vertices represents a surface in $S\\times \\mathbb{R}$, and a simple algorithm for constructing minimal genus surfaces of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4206","kind":"arxiv","version":4},"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"}