Borel density for approximate lattices
Group Theory
2019-12-04 v1 Dynamical Systems
Abstract
We extend classical density theorems of Borel and Dani--Shalom on lattices in semisimple, respectively solvable algebraic groups over local fields to approximate lattices. Our proofs are based on the observation that Zariski closures of approximate subgroups are close to algebraic subgroups. Our main tools are stationary joinings between the hull dynamical systems of discrete approximate subgroups and their Zariski closures.
Cite
@article{arxiv.1902.10560,
title = {Borel density for approximate lattices},
author = {Michael Björklund and Tobias Hartnick and Thierry Stulemeijer},
journal= {arXiv preprint arXiv:1902.10560},
year = {2019}
}
Comments
17 pages, 0 figures. Comments are welcome!