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

Abstract

The works of Donaldson (2) and Mark (14) 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.