PreprintCC0arXiv
Counterexamples to the continuous Aldous-Lyons conjecture
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].
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BibTeX
@misc{gelander2026counterexamples,
title = {{Counterexamples to the continuous Aldous-Lyons conjecture}},
author = {Tsachik Gelander},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08581},
eprint = {2610.08581},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08581},
note = {CC0},
}
RIS
TY - UNPB
TI - Counterexamples to the continuous Aldous-Lyons conjecture
AU - Tsachik Gelander
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.08581
UR - https://arxiv.org/abs/2610.08581
AB - 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].
ER -