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

Schuetz, D. (2002) 'One-parameter fixed-point theory and gradient flows of closed 1-forms.', K-theory., 25 (1). pp. 59-97.


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 completed simplicial chain complex of the universal cover of M.

Item Type:Article
Keywords:One-parameter fixed-point theory, Closed 1-forms, Zeta function, Novikov complex.
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Date of first online publication:January 2002
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