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

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

2007-09-20

arxiv.org/abs/0709.3153v2

Mathematics

Geometric Topology

27 pages, 12 figures

Scientific paper

The works of Donaldson and Mark make 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. We study these invariants using the Morse-Novikov theory and Heegaard splitting for sutured manifolds, and make detailed computations for knot complements.

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