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

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.

Cited by in corpus (8)

• Noncommutative localisation in algebraic K-theory I
• Closed orbits of gradient flows and logarithms of non-abelian Witt vectors
• Controlled connectivity of closed 1-forms
• Twisted Morse complexes
• Conley Index Theory and Novikov-Morse Theory
• One parameter fixed point theory and gradient flows of closed 1-forms
• Gradient flows of closed 1-forms and their closed orbits
• Morse Novikov theory and cohomology with forward supports