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The Morse-Novikov theory of circle-valued functions and noncommutative localization

Michael Farber·Andrew Ranicki
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Abstract

We use noncommutative localization to construct a chain complex which counts the critical points of a circle-valued Morse function on a manifold, generalizing the Novikov complex. As a consequence we obtain new topological lower bounds on the minimum number of critical points of a circle-valued Morse function within a homotopy class, generalizing the Novikov inequalities.

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Michael Farber, Andrew Ranicki. 1998-12-21. The Morse-Novikov theory of circle-valued functions and noncommutative localization. https://arxiv.org/abs/math/9812122

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