{"paper":{"title":"An algebraic generalization of Giroux's criterion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Russell Avdek","submitted_at":"2023-07-18T08:38:09Z","abstract_excerpt":"Let $\\xi$ be a $\\tau$-invariant contact structure on $N(W) = \\mathbb{R}_{\\tau} \\times W$ for a closed, $2n$-dimensional manifold $W$, so that each $\\{\\tau\\} \\times W$ is a convex hypersurface. When $n=1$, Giroux's criterion provides a simple means of determining exactly when $\\xi$ is tight. It is an open problem to find a generalization applicable for $n>1$. This article solves an algebraic version of the problem, determining exactly when $(N(W), \\xi)$ has non-vanishing contact homology ($CH$) and computing $CH(N(W), \\xi)$ when it is non-zero. The result can be expressed in terms of homotopy e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.09068","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.09068/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"}