Circle-valued Morse theory, Reidemeister torsion, and Seiberg-Witten invariants of 3-manifolds

Michael Hutchings, Yi-Jen Lee

Let X be a compact oriented Riemannian manifold and let $\varphi :X\to S^1$ be a circle-valued Morse function. Under some mild assumptions on $\varphi$, we prove a formula relating: (a) the num…