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

2007/09/20 by Hiroshi Goda, Goda, Hiroshi, Hiroshi Matsuda +3
Mathematics · #57M25 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.DG #math.GT #msc:57M25

paper · pdf · doi:10.48550/arxiv.0709.3153

27 pages, 12 figures

arxiv created 2009/07/16 · arxiv updated 2009/12/01

Abstract

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.

Related

• Circle-valued Morse theory, Reidemeister torsion, and Seiberg-Witten\n invariants of 3-manifolds
• Knot as a complete invariant of a Morse-Smale 3-diffeomorphism with four fixed points
• Morse flows with fixed points on the boundary of 3-manifold
• Counting closed orbits of gradients of circle-valued maps
• Gradient flows of closed 1-forms and their closed orbits