Gradient flows of closed 1-forms and their closed orbits

Details Gradient flows of closed 1-forms and their closed orbits Gradient flows of closed 1-forms and their closed orbits

2000-09-06

arxiv.org/abs/math/0009055v2

Forum Math. 14 (2002) 509-537

Mathematics

Differential Geometry

26 pages, 2 figures, Latex, to appear in Forum Mathematicum

Scientific paper

We consider the closed orbit structure of generic gradient flows of Morse
closed 1-forms. The torsion of a chain homotopy equivalence between the Novikov
complex and the completed simplicial chain complex of the universal cover
detects the eta function of the flow. We extend this result to arbitrary Morse
closed 1-forms. The case of rational forms was considered by A. Pajitnov.

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