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

D. Schuetz
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Abstract

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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D. Schuetz. 2001-04-25. One parameter fixed point theory and gradient flows of closed 1-forms. https://arxiv.org/abs/math/0104245

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