{"paper":{"title":"The Gompf $\\theta$-Invariant of Canonical Contact Structures via Legendrian Surgery","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Burak Ozbagci, Mohan Bhupal","submitted_at":"2026-05-20T13:25:08Z","abstract_excerpt":"Let $\\Gamma$ be a minimal connected negative-definite plumbing tree with all vertices of genus zero, and let $Y_\\Gamma$ be the oriented link of the corresponding normal complex surface singularity, equipped with its canonical contact structure $\\xi_{\\rm can}$. We give an explicit Legendrian surgery description of $\\xi_{\\rm can}$, showing that it is the unique consistent diagram-realizable contact structure on $Y_\\Gamma$, up to isomorphism. We then derive a closed-form formula for Gompf's $\\theta$-invariant of $\\xi_{\\rm can}$ in the Seifert fibered case, expressed purely in terms of the Hirzebr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21152","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.21152/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"}