#### Volume 20, issue 5 (2016)

 Recent Issues
 The Journal About the Journal Editorial Board Subscriptions Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Author Index To Appear Other MSP Journals
Using simplicial volume to count maximally broken Morse trajectories

### Hannah Alpert

Geometry & Topology 20 (2016) 2997–3018
##### Abstract

Given a closed Riemannian manifold of dimension $n$ and a Morse–Smale function, there are finitely many $n$–part broken trajectories of the negative gradient flow. We show that if the manifold admits a hyperbolic metric, then the number of $n$–part broken trajectories is always at least the hyperbolic volume. The proof combines known theorems in Morse theory with lemmas of Gromov about simplicial volumes of stratified spaces.

##### Keywords
simplicial volume, Gromov norm, hyperbolic volume, Morse–Smale vector field, Morse broken trajectories
##### Mathematical Subject Classification 2000
Primary: 53C23
Secondary: 58E05, 57N80