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Algebra i Analiz, 2014, Volume 26, Issue 3, Pages 131–158 (Mi aa1386)  

Research Papers

Morse–Novikov theory, Heegaard splittings, and closed orbits of gradient flows

H. Godaa, H. Matsudab, A. Pajitnovc

a Department of Mathematics, Tokyo University of Agriculture and Technology, 2-24-16 Naka-cho, Koganei, Tokyo 184-8588, Japan
b Department of Mathematical Sciences, Yamagata University, Yamagata 990-8560, Japan
c Laboratoire de Mathématiques, Jean-Leray UMR 6629, Université de Nantes, Faculté des Sciences, 2, rue de la Houssinière, 44072, Nantes, Cedex, France

Abstract: The work of Donaldson and Mark made the structure of the Seiberg–Witten invariant of $3$-manifolds clear. It corresponds to certain torsion type invariants counting flow lines and closed orbits of a gradient flow of a circle-valued Morse map on a $3$-manifold. In the paper, these invariants are studied by using the Morse–Novikov theory and Heegaard splitting for sutured manifolds, and detailed computations are made for knot complements.

Keywords: oriented knot, sutured manifold, Morse map, Novikov complex, half-transversal gradients, Lefschetz zeta function.

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English version:
St. Petersburg Mathematical Journal, 2015, 26:3, 441–461

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Received: 02.03.2013
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Citation: H. Goda, H. Matsuda, A. Pajitnov, “Morse–Novikov theory, Heegaard splittings, and closed orbits of gradient flows”, Algebra i Analiz, 26:3 (2014), 131–158; St. Petersburg Math. J., 26:3 (2015), 441–461

Citation in format AMSBIB
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\by H.~Goda, H.~Matsuda, A.~Pajitnov
\paper Morse--Novikov theory, Heegaard splittings, and closed orbits of gradient flows
\jour Algebra i Analiz
\yr 2014
\vol 26
\issue 3
\pages 131--158
\mathnet{http://mi.mathnet.ru/aa1386}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3289179}
\elib{https://elibrary.ru/item.asp?id=22834088}
\transl
\jour St. Petersburg Math. J.
\yr 2015
\vol 26
\issue 3
\pages 441--461
\crossref{https://doi.org/10.1090/S1061-0022-2015-01345-9}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000357043800003}


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