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Research Article | Open Access

Remarks on the end-topology of some discrete groups

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

Keywords

topology at infinitydiscrete groupshyperbolic spacesCayley graphsgrowth
CLC number: 20F05, 20F67, 20F69

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AIMS Mathematics
Volume 8 Issue 9,
September 2023
Pages 20143-20153
DOI: 10.3934/math.20231026

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Otera DE. Remarks on the end-topology of some discrete groups. AIMS Mathematics, 2023, 8(9): 20143-20153. https://doi.org/10.3934/math.20231026

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Received: 07 April 2023
Revised: 10 June 2023
Accepted: 13 June 2023
Published: 15 September 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)