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

2001/04/25 by D. Schuetz
Mathematics · #math.DG #msc:37C27 #msc:57R70

paper · pdf

published as K-Theory 25 (2002) 59-97 · 33 pages, Latex

arxiv created 2001/04/25 · arxiv updated 2009/11/30

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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