Circle-Valued Morse Theory and Reidemeister Torsion
نویسنده
چکیده
We compute an invariant counting gradient flow lines (including closed orbits) in S-valued Morse theory, and relate it to Reidemeister torsion for manifolds with χ = 0, b1 > 0. Here we extend the results in [6] following a different approach. However, this paper is written in a self-contained manner and may be read independently of [6]. The motivation of this work is twofold: on the one hand, it relates algebraic counting of gradient flow lines with topological invariants of the manifold; on the other hand, its application to the three-dimensional case yields the equivalence of the Seiberg-Witten invariants of three-manifolds and Reidemeister torsion, up to the highly likely Conjecture 1. This refines the Meng-Taubes theorem in [10].
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