Morse subsets of injective spaces are strongly contracting

A Sisto, A Zalloum - Groups, Geometry, and Dynamics, 2024 - ems.press
We show that a quasi-geodesic in an injective metric space is Morse if and only if it is
strongly contracting. Since mapping class groups and, more generally, hierarchically …

Regularity of Morse geodesics and growth of stable subgroups

M Cordes, J Russell, D Spriano… - Journal of Topology, 2022 - Wiley Online Library
We prove that Morse local‐to‐global groups grow exponentially faster than their infinite‐
index stable subgroups. This generalizes a result of Dahmani, Futer, and Wise in the context …

Counting conjugacy classes in groups with contracting elements

I Gekhtman, W Yang - Journal of Topology, 2022 - Wiley Online Library
In this paper, we derive an asymptotic formula for the number of conjugacy classes of
elements in a class of statistically convex‐cocompact actions with contracting elements …

Sigma-compactness of Morse boundaries in Morse local-to-global groups and applications to stationary measures

V He, D Spriano, S Zbinden - arXiv preprint arXiv:2407.18863, 2024 - arxiv.org
We show that the Morse boundary of a Morse local-to-global group is $\sigma $-compact.
Moreover, we show that the converse holds for small cancellation groups. As an application …

Counting conjugacy classes in groups with contracting elements

I Gekhtman, W Yang - arXiv preprint arXiv:1810.02969, 2018 - arxiv.org
In this paper, we derive an asymptotic formula for the number of conjugacy classes of
elements in a class of statistically convex-cocompact actions with contracting elements …