Random Gromov’s monsters do not act non-elementarily on hyperbolic spaces-Reference-Cited by-同舟云学术

Random Gromov’s monsters do not act non-elementarily on hyperbolic spaces

Published:2020-03-18 Issue:7 Volume:148 Page:2773-2782
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Gruber Dominik,Sisto Alessandro,Tessera Romain

Abstract

We show that Gromov’s monster groups arising from i.i.d. labelings of expander graphs do not admit non-elementary actions on geodesic hyperbolic spaces. The proof relies on comparing properties of random walks on randomly labeled graphs and on groups acting non-elementarily on hyperbolic spaces.

Funder

Eidgenössische Technische Hochschule Zürich

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

https://www.ams.org/proc/2020-148-07/S0002-9939-2020-14754-5/proc14754_AM.pdf

Reference22 articles.

1. [AD08] G. Arzhantseva and T. Delzant, Examples of random groups, preprint. 2008, available from the authors’ websites.

2. Wiley-Interscience Series in Discrete Mathematics and Optimization;Alon, Noga,2000

3. Acylindrical group actions on quasi-trees;Balasubramanya, Sahana H.;Algebr. Geom. Topol.,2017

4. Property (T) and rigidity for actions on Banach spaces;Bader, Uri;Acta Math.,2007

5. Cohomologie et actions isométriques propres sur les espaces 𝐿^{𝑝}, Geometry, Topology, and Dynamics in Negative Curvature (Bangalore 2010);Bourdon, M.,2016

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Random walks on mapping class groups;EMS Surveys in Mathematical Sciences;2023-10-24

2. Divergence and quasi-isometry classes of random Gromov’s monsters;Mathematical Proceedings of the Cambridge Philosophical Society;2021-02-18

3. Random walks, WPD actions, and the Cremona group;Proceedings of the London Mathematical Society;2021-01-04

4. Counting problems in graph products and relatively hyperbolic groups;Israel Journal of Mathematics;2020-05-14