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

Goda, H.; Matsuda, H.; Pajitnov, A.

doi:10.1090/S1061-0022-2015-01345-9

Morse–Novikov theory, Heegaard splittings, and closed orbits of gradient flows
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by H. Goda, H. Matsuda and A. Pajitnov

St. Petersburg Math. J. 26 (2015), 441-461

DOI: https://doi.org/10.1090/S1061-0022-2015-01345-9

Published electronically: March 20, 2015

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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.

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