{"paper":{"title":"Floer homology and surface decompositions","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Andras Juhasz","submitted_at":"2006-09-28T04:01:49Z","abstract_excerpt":"Sutured Floer homology, denoted by SFH, is an invariant of balanced sutured manifolds previously defined by the author. In this paper we give a formula that shows how this invariant changes under surface decompositions. In particular, if (M, \\gamma)--> (M', \\gamma') is a sutured manifold decomposition then SFH(M',\\gamma') is a direct summand of SFH(M, \\gamma). To prove the decomposition formula we give an algorithm that computes SFH(M,\\gamma) from a balanced diagram defining (M,\\gamma) that generalizes the algorithm of Sarkar and Wang.\n  As a corollary we obtain that if (M, \\gamma) is taut the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609779","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"}