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

Hiroshi Goda , Hiroshi Matsuda , Andrei Pajitnov (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

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.

Domaines: Topologie géométrique [math.GT]; Géométrie différentielle [math.DG]

Hiroshi Goda, Hiroshi Matsuda, Andrei Pajitnov. Morse-Novikov theory, Heegaard splittings and closed orbits of gradient flows. 2009. ⟨hal-00870278⟩