Counting maximally broken Morse trajectories on aspherical manifolds

TL;DR

This paper establishes a lower bound on the number of maximally broken Morse trajectories on aspherical manifolds, linking dynamical flow behavior to the manifold's integral homology.

Contribution

It introduces a novel lower bound relating Morse flow trajectories to integral (torsion) homology on aspherical manifolds.

Findings

Lower bound on broken Morse trajectories established

Connection between flow trajectories and homology proven

Results applicable to aspherical manifolds

Abstract

We prove a lower bound on the number of maximally broken trajectories of the negative gradient flow of a Morse-Smale function on a closed aspherical manifold in terms of integral (torsion) homology.