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

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

1998-12-21

arxiv.org/abs/math/9812122v1

Mathematics

Differential Geometry

Scientific paper

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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