Qualitative counting closed geodesics
Differential Geometry
2021-06-28 v2 Group Theory
Geometric Topology
Abstract
We investigate the geometry of word metrics on fundamental groups of manifolds associated with the generating sets consisting of elements represented by closed geodesics. We ask whether the diameter of such a metric is finite or infinite. The first answer we interpret as an abundance of closed geodesics, while the second one as their scarcity. We discuss examples for both cases.
Cite
@article{arxiv.1904.11237,
title = {Qualitative counting closed geodesics},
author = {Bastien Karlhofer and Jarek Kędra and Michał Marcinkowski and Alexander Trost},
journal= {arXiv preprint arXiv:1904.11237},
year = {2021}
}
Comments
10 pages