Year: 2026
Type: preprint
Abstract: We construct non-co-sofic invariant random subgroups in connected simple real Lie groups of rank one with finite center, in Zariski connected simple rank-one groups over non-Archimedean local fields, and in Aut(T) for regular and bi-regular trees T. This gives a negative answer to the continuous analogue of the classical Aldous-Lyons conjecture for these groups. Our constructions build on the existence of a finitely generated non-sofic group and answer a question raised in the author's ICM paper [Gel18].
Source: arXiv (Cornell University)
Author: Gelander, Tsachik
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7221033490