{"paper":{"title":"The Kodaira dimension of contact 3-manifolds and geography of symplectic fillings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Cheuk Yu Mak, Tian-Jun Li","submitted_at":"2016-10-21T17:35:17Z","abstract_excerpt":"We introduce the Kodaira dimension of contact 3-manifolds and establish some basic properties. In particular, contact 3-manifolds with distinct Kodaria dimensions behave differently when it comes to the geography of various kinds of fillings. On the other hand, we also prove that, given any contact 3-manifold, there is a lower bound of $2\\chi+3\\sigma$ for all its minimal symplectic fillings. This is motivated by the bound of Stipsicz for Stein fillings. Finally, we discuss various aspects of exact self cobordisms of fillable 3-manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06870","kind":"arxiv","version":1},"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"}