  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.
