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

Schuetz, Dirk

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 completed simplicial chain complex of the universal cover of M.

Citation

Schuetz, D. (2002). One-parameter fixed-point theory and gradient flows of closed 1-forms. K-Theory, 25(1), 59-97. https://doi.org/10.1023/a%3A1015079805400

• Journal Article Type: Article
• Publication Date: Jan 1, 2002
• Deposit Date: Mar 27, 2008
• Journal: K-Theory
• Print ISSN: 0920-3036
• Electronic ISSN: 1573-0514
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 25
• Issue: 1
• Pages: 59-97
• DOI: https://doi.org/10.1023/a%3A1015079805400
• Keywords: One-parameter fixed-point theory, Closed 1-forms, Zeta function, Novikov complex.
• Public URL: https://durham-repository.worktribe.com/output/1593565