{"paper":{"title":"Tight contact structures on some bounded Seifert manifolds with minimal convex boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Fan Ding, Qiang Zhang, Youlin Li","submitted_at":"2011-11-08T13:21:04Z","abstract_excerpt":"We classify positive tight contact structures, up to isotopy fixing the boundary, on the manifolds $N=M(D^{2}; r_1, r_2)$ with minimal convex boundary of slope $s$ and Giroux torsion 0 along $\\partial N$, where $r_1,r_2\\in (0,1)\\cap\\mathbb{Q}$, in the following cases:\n  (1) $s\\in(-\\infty, 0)\\cup[2, +\\infty)$;\n  (2) $s\\in[0, 1)$ and $r_1,r_2\\in [1/2,1)$;\n  (3) $s\\in[1, 2)$ and $r_1,r_2\\in(0,1/2)$;\n  (4) $s=\\infty$ and $r_1=r_2=1/2$.\n  We also classify positive tight contact structures, up to isotopy fixing the boundary, on $M(D^2;1/2,1/2)$ with minimal convex boundary of arbitrary slope and Gir"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1900","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"}