{"paper":{"title":"Small symplectic $4$-manifolds via contact gluing and some applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.SG"],"primary_cat":"math.GT","authors_text":"Weimin Chen","submitted_at":"2025-03-07T20:58:03Z","abstract_excerpt":"We introduce a streamlined procedure for constructing small symplectic $4$-manifolds via contact gluing, based on a technique invented by David Gay around 2000. We give several applications of this procedure, which include results concerning embeddings of singular Lagrangian $RP^2$s, or embeddings of lens spaces as a hypersurface of contact type, in small rational surfaces such as $CP^2\\#\\overline{CP^2}$ and $S^2\\times S^2$, as well as results on the uniqueness or classification of $Q$-homology ball symplectic fillings. Further work on the classification of singular Lagrangian $RP^2$s is sugge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.05932","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.05932/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}