One-Parameter Fixed-Point Theory and Gradient Flows of Closed 1-Forms |
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Authors: | D Schütz |
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Institution: | (1) Department of Mathematics, SUNY Binghamton, Binghamton, NY, 13902-6000, U.S.A |
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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 completed simplicial chain complex of the universal cover of M. |
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Keywords: | One-parameter fixed-point theory Closed 1-forms Zeta function Novikov complex |
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