Remarks on the end-topology of some discrete groups

Daniele Ettore Otera; Daniele Ettore Otera

doi:10.3934/math.20231026

AIMS Mathematics

2023, Volume 8, Issue 9: 20143-20153. doi: 10.3934/math.20231026

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Remarks on the end-topology of some discrete groups

Daniele Ettore Otera ^,

Institute of Data Science and Digital Technologies, Vilnius University, Akademijos st. 4, LT-08663, Vilnius, Lithuania

Received: 07 April 2023 Revised: 10 June 2023 Accepted: 13 June 2023 Published: 19 June 2023
MSC : 20F05, 20F67, 20F69

In this note we consider the notion of rate of vanishing of the simple connectivity at infinity, a (growth) function that estimates metrically the topology at infinity of metric spaces. In particular we provide a different (geometric) proof of the linearity of the sci-growth for hyperbolic groups.
- topology at infinity,
- discrete groups,
- hyperbolic spaces,
- Cayley graphs,
- growth
Citation: Daniele Ettore Otera. Remarks on the end-topology of some discrete groups[J]. AIMS Mathematics, 2023, 8(9): 20143-20153. doi: 10.3934/math.20231026

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Abstract

In this note we consider the notion of rate of vanishing of the simple connectivity at infinity, a (growth) function that estimates metrically the topology at infinity of metric spaces. In particular we provide a different (geometric) proof of the linearity of the sci-growth for hyperbolic groups.

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