Circle-valued Morse theory

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In mathematics, circle-valued Morse theory studies the topology of a smooth manifold by analyzing the critical points of smooth maps from the manifold to the circle, in the framework of Morse homology.[1] It is an important special case of Sergei Novikov's Morse theory of closed one-forms.[2]

Michael Hutchings and Yi-Jen Lee have connected it to Reidemeister torsion and Seiberg–Witten theory.[3]


  1. ^ Pajitnov, Andrei V. (2006), Circle-valued Morse theory, de Gruyter Studies in Mathematics, 32, Walter de Gruyter & Co., Berlin, doi:10.1515/9783110197976, ISBN 978-3-11-015807-6, MR 2319639 .
  2. ^ Farber, Michael (2004), Topology of closed one-forms, Mathematical Surveys and Monographs, 108, American Mathematical Society, Providence, RI, p. 50, doi:10.1090/surv/108, ISBN 0-8218-3531-9, MR 2034601 .
  3. ^ Hutchings, Michael; Lee, Yi-Jen (1999), "Circle-valued Morse theory, Reidemeister torsion, and Seiberg-Witten invariants of 3-manifolds", Topology, 38 (4): 861–888, doi:10.1016/S0040-9383(98)00044-5, MR 1679802 .