One parameter fixed point theory and gradient flows of closed 1forms
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 1forms 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 1form 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 2001
 arXiv:
 arXiv:math/0104245
 Bibcode:
 2001math......4245S
 Keywords:

 Differential Geometry;
 37C27 (primary) 57R70 (secondary)
 EPrint:
 33 pages, Latex