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Weak Morse properties in spaces with bounded combings
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Weak Morse properties in spaces with bounded combings
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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.
Forward citations
Cited by 2 Pith papers
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Groups with navigable path systems satisfy weak rank rigidity and the Morse local-to-global property, proved uniformly via a new generalised contraction space.
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A group has σ-compact Morse boundary precisely when it satisfies the Morse local-to-global property, enabling construction of the first non-virtually cyclic example with an infinite-order Morse element outside acylind...
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