{"paper":{"title":"Geometry of the Homology Curve Complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Ingrid Irmer","submitted_at":"2011-07-18T19:53:47Z","abstract_excerpt":"Suppose $S$ is a closed, oriented surface of genus at least two. This paper investigates the geometry of the homology multicurve complex, $\\mathcal{HC}(S,\\alpha)$, of $S$; a complex closely related to complexes studied by Bestvina-Bux-Margalit and Hatcher. A path in $\\mathcal{HC}(S,\\alpha)$ corresponds to a homotopy class of immersed surfaces in $S\\times I$. This observation is used to devise a simple algorithm for constructing quasi-geodesics connecting any two vertices in $\\mathcal{HC}(S,\\alpha)$, and for constructing minimal genus surfaces in $S\\times I$. It is proven that for $g \\geq 3$ th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3547","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"}