Weak Morse properties in spaces with bounded combings
Group Theory
2025-03-28 v1 Metric Geometry
Abstract
We relate two notions of non-positive curvature: bounded combings and the Morse local-to-global (MLTG) property (in its weak and strong version). The latter is a property of a space that has been shown to eliminate pathological behavior of Morse geodesics. We showcase its importance in a survey in the appendix. We show that having a bounded combing implies the weak MLTG property. If the Morse boundary of a group is sigma-compact, we show that the weak MLTG property is upgraded to the (strong) MLTG property.
Keywords
Cite
@article{arxiv.2503.21325,
title = {Weak Morse properties in spaces with bounded combings},
author = {Cornelia Drutu and Davide Spriano and Stefanie Zbinden},
journal= {arXiv preprint arXiv:2503.21325},
year = {2025}
}
Comments
30 pages (20 paper, 10 appendix), 8 figures