Spectral gap and origami expanders
Metric Geometry
2024-02-27 v3 Dynamical Systems
Group Theory
Geometric Topology
Abstract
We construct the first measure-preserving affine actions with spectral gap on surfaces of arbitrary genus . We achieve this by finding geometric representatives of multi-twists on origami surfaces. As a major application, we construct new expanders that are coarsely distinct from the classical expanders obtained via the Laplacian as Cayley graphs of finite quotients of a group. Our methods also show that the Margulis expander, and hence the Gabber--Galil expander, is coarsely distinct from the Selberg expander.
Keywords
Cite
@article{arxiv.2112.11864,
title = {Spectral gap and origami expanders},
author = {Goulnara Arzhantseva and Dawid Kielak and Tim de Laat and Damian Sawicki},
journal= {arXiv preprint arXiv:2112.11864},
year = {2024}
}
Comments
To appear in the Commentarii Mathematici Helvetici