{"paper":{"title":"Contact Structures on Plumbed 3-Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Cagri Karakurt","submitted_at":"2009-10-20T21:13:15Z","abstract_excerpt":"In this paper, we show that the Ozsv\\'ath-Szab\\'o contact invariant $c^+(\\xi)\\in HF^+(-Y)$ of a contact 3-manifold $(Y,\\xi)$ can be calculated combinatorially if $Y$ is the boundary of a certain type of plumbing $X$, and $\\xi$ is induced by a Stein structure on $X$. Our technique uses an algorithm of Ozsv\\'ath and Szab\\'o to determine the Heegaard-Floer homology of such 3-manifolds. We discuss two important applications of this technique in contact topology. First, we show that it simplifies the calculation of the Ozsv\\'ath-Stipsicz-Szab\\'o obstruction to admitting a planar open book. Then we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.3965","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"}