Genericity of contracting geodesics in groups

Kunal Chawla; Inhyeok Choi; Giulio Tiozzo

doi:10.4171/ggd/902

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Genericity of contracting geodesics in groups

Kunal Chawla
Princeton University, USA
ORCID
Inhyeok Choi
Cornell University, Ithaca, USA; Korea Institute for Advanced Study, Seoul, South Korea
ORCID
Giulio Tiozzo
University of Toronto, Canada
ORCID

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Abstract

Let $G$ be a finitely generated group and $Cay (G, S)$ be the Cayley graph of $G$ with respect to a finite generating set $S$ . We characterize the Gromov hyperbolicity of $G$ in terms of the genericity of contracting elements in $Cay (G, S)$ .

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Kunal Chawla, Inhyeok Choi, Giulio Tiozzo, Genericity of contracting geodesics in groups. Groups Geom. Dyn. (2025), published online first

DOI 10.4171/GGD/902