Geodesic
Morse--Novikov theory, Heegaard splittings, and closed orbits of gradient flows
Algebra i analiz, Tome 26 (2014) no. 3, pp. 131-158.

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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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H. Goda; H. Matsuda; A. Pajitnov. Morse--Novikov theory, Heegaard splittings, and closed orbits of gradient flows. Algebra i analiz, Tome 26 (2014) no. 3, pp. 131-158. http://geodesic.mathdoc.fr/item/AA_2014_26_3_a2/

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