Work

Confined subgroups in groups with contracting elements

Year: 2024

Type: preprint

Abstract: In this paper, we study the growth of confined subgroups through boundary actions of groups with contracting elements. We establish that the growth rate of a confined subgroup is strictly greater than half of the ambient growth rate in groups with purely exponential growth. Along the way, several results are obtained on the Hopf decomposition for boundary actions of subgroups with respect to conformal measures. In particular, we prove that confined subgroups are conservative, and examples of subgroups with nontrivial Hopf decomposition are constructed. We show a connection between Hopf decomposition and quotient growth and provide a dichotomy on quotient growth of Schreier graphs for subgroups in hyperbolic groups.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2405.09070

Authors: Choi, Inhyeok, Gekhtman, Ilya, Yang, Wenyuan, Zheng, Tianyi

Institutions: Korea Institute for Advanced Study, University of California San Diego, Peking University, Peking University International Hospital, Beijing International Studies University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Samsung, Division of Mathematical Sciences

Awards: G7483175396, G8358677156

OpenAlex ID: W4396986819

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