{"paper":{"title":"3-manifolds Modulo Surgery Triangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Lucas Culler","submitted_at":"2014-10-14T16:23:18Z","abstract_excerpt":"Surgery triangles are an important computational tool in Floer homology. Given a connected oriented surface $\\Sigma$, we consider the abelian group $K(\\Sigma)$ generated by bordered 3-manifolds with boundary $\\Sigma$, modulo the relation that the three manifolds involved in any surgery triangle sum to zero. We show that $K(\\Sigma)$ is a finitely generated free abelian group and compute its rank. We also construct an explicit basis and show that it generates all bordered 3-manifolds in a certain stronger sense. Our basis is strictly contained in another finite generating set which was construct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3755","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"}