English

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

R2 v1 2026-06-28T22:36:26.848Z