Confined subgroups in groups with contracting elements
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914796585091072 |
|---|---|
| author | Choi, Inhyeok Gekhtman, Ilya Yang, Wenyuan Zheng, Tianyi |
| author_facet | Choi, Inhyeok Gekhtman, Ilya Yang, Wenyuan Zheng, Tianyi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09070 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Confined subgroups in groups with contracting elements Choi, Inhyeok Gekhtman, Ilya Yang, Wenyuan Zheng, Tianyi Group Theory Dynamical Systems Geometric Topology 20F65, 20F67, 20F69 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. |
| title | Confined subgroups in groups with contracting elements |
| topic | Group Theory Dynamical Systems Geometric Topology 20F65, 20F67, 20F69 |
| url | https://arxiv.org/abs/2405.09070 |