{"paper":{"title":"Circle-valued Morse theory, Reidemeister torsion, and Seiberg-Witten invariants of 3-manifolds","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"dg-ga","authors_text":"Michael Hutchings, Yi-Jen Lee","submitted_at":"1996-12-03T17:58:11Z","abstract_excerpt":"Let X be a compact oriented Riemannian manifold and let $\\phi:X\\to S^1$ be a circle-valued Morse function. Under some mild assumptions on $\\phi$, we prove a formula relating:\n  (a) the number of closed orbits of the gradient flow of $\\phi$ of any given degree;\n  (b) the torsion of a ``Morse complex'', which counts gradient flow lines between critical points of $\\phi$; and\n  (c) a kind of Reidemeister torsion of X determined by the homotopy class of $\\phi$.\n  When $\\dim(X)=3$ and $b_1(X)>0$, we state a conjecture analogous to Taubes's ``SW=Gromov'' theorem, and we use it to deduce (for closed m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"dg-ga/9612004","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":""},"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"}