Genericity of contracting geodesics in groups

Kunal Chawla; Inhyeok Choi; Giulio Tiozzo

doi:10.4171/ggd/902

July 29, 2025Groups Geometry and DynamicsOpen Access

Genericity of contracting geodesics in groups

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Key Points

The characterization of gromov hyperbolicity is achieved using contracting elements in Cayley graphs.
Cayley graphs play a crucial role in understanding the geometric properties of finitely generated groups.
Finding generic contracting elements provides insight into the structural aspects of these groups.
Understanding gromov hyperbolicity has implications for the study of geometric group theory.

Implication

This paper characterizes gromov hyperbolicity through the genericity of contracting elements in Cayley graphs.

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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Cite This Study

Chawla et al. (2025) studied this question.

synapsesocial.com/papers/68c19f7f54b1d3bfb60dad69 https://doi.org/10.4171/ggd/902

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Genericity of contracting geodesics in groups

Key Points

Implication

Abstract

Discussion

Cite This Study

Genericity of contracting geodesics in groups

Key Points

Implication

Abstract

Discussion

Cite This Study

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