The Morse-Novikov theory of circle-valued functions and noncommutative localization
Differential Geometry
2007-05-23 v1 Algebraic Topology
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.
Keywords
Cite
@article{arxiv.math/9812122,
title = {The Morse-Novikov theory of circle-valued functions and noncommutative localization},
author = {Michael Farber and Andrew Ranicki},
journal= {arXiv preprint arXiv:math/9812122},
year = {2007}
}