One parameter fixed point theory and gradient flows of closed 1-forms

Details One parameter fixed point theory and gradient flows of closed 1-forms One parameter fixed point theory and gradient flows of closed 1-forms

2001-04-25

arxiv.org/abs/math/0104245v1

K-Theory 25 (2002) 59-97

Mathematics

Differential Geometry

33 pages, Latex

Scientific paper

We use the one parameter fixed point theory of Geoghegan and Nicas to get information about the closed orbit structure of transverse gradient flows of closed 1-forms on a closed manifold M. We define a noncommutative zeta function in an object related to the first Hochschild homology group of the Novikov ring associated to the 1-form and relate it to the torsion of a natural chain homotopy equivalence between the Novikov complex and a simplicial complex of the universal cover of M.

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