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arXiv · 2503.21325

Weak Morse properties in spaces with bounded combings

Cornelia Drutu·Davide Spriano·Stefanie Zbinden
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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.

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Cornelia Drutu, Davide Spriano, Stefanie Zbinden. 2025-03-27. Weak Morse properties in spaces with bounded combings. https://arxiv.org/abs/2503.21325

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