{"paper":{"title":"Recovering contact forms from boundary data","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.SG","authors_text":"Gabriel Katz","submitted_at":"2023-09-26T01:22:32Z","abstract_excerpt":"Let $X$ be a compact smooth manifold with boundary. The paper deals with contact $1$-forms $\\beta$ on $X$, whose Reeb vector fields $v_\\beta$ admit Lyapunov functions $f$.\n  We tackle the question: how to recover $X$ and $\\beta$ from the appropriate data along the boundary $\\partial X$? We describe such boundary data and prove that they allow for a reconstruction of the pair $(X, \\beta)$, up to a diffeomorphism of $X$. We use the term ``holography\" for the reconstruction. We say that objects or structures inside $X$ are {\\it holographic}, if they can be reconstructed from their $v_\\beta$-flow "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.14604","kind":"arxiv","version":7},"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/2309.14604/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"}