{"paper":{"title":"Morse flow categories as exit path categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.SG"],"primary_cat":"math.AT","authors_text":"Colin Fourel","submitted_at":"2026-05-26T14:52:01Z","abstract_excerpt":"We prove that the topological flow category $\\mathcal{M}$ arising from a Morse-Smale pair $(f,\\xi)$ on a smooth closed manifold $X$ is equivalent, as an $\\infty$-category, to Lurie's $\\infty$-category $\\mathrm{Sing}_A(X)$ of exit paths in $X$ with respect to the stratification by the stable manifolds of $\\xi$.\n  The objects of $\\mathcal{M}$ are the critical points of $f$, and for every pair of critical points, the space of morphisms of $\\mathcal{M}$ between these is the space of possibly broken trajectories of $\\xi$ connecting them; it can be identified up to homotopy with the space of unbroke"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27112","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/2605.27112/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"}