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arXiv · 1902.10560

Borel density for approximate lattices

Michael Björklund·Tobias Hartnick·Thierry Stulemeijer
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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.

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Michael Björklund, Tobias Hartnick, Thierry Stulemeijer. 2019-02-27. Borel density for approximate lattices. https://doi.org/10.1017/fms.2019.39

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