5 papers
Quasihomomorphisms to real algebraic groups
Sami Douba, Francesco Fournier-Facio, Sam Hughes +1
A quasihomomorphism is a map that satisfies the homomorphism relation up to bounded error. Fujiwara and Kapovich proved a rigidity result for quasihomomorphisms taking values in di…
Asymmetric stability of the Brunn--Minkowski inequality in compact Lie groups
Simon Machado
We show a stability result for the recently established Brunn--Minkowski inequality in compact simple Lie groups. Namely, we prove that if two compact subsets of a compact s…
Minimal doubling for small subsets in compact Lie groups
Simon Machado
We prove a sharp bound for the minimal doubling of a small measurable subset of a compact connected Lie group. Namely, let be a compact connected Lie group of dimension ,…
The definitions of approximate lattices
Simon Machado
Approximate lattices of locally compact groups were first studied in a seminal monograph of Yves Meyer and were subsequently used in the theory of aperiodic order to model objects…
Approximate lattices and S-adic linear groups
Simon Machado
We provide and motivate in this paper a natural framework for the study of approximate lattices. Namely, we consider approximate lattices in so-called -adic linear groups and de…