Spectral gap and origami expanders
Goulnara Arzhantseva
Universität Wien, Wien, AustriaDawid Kielak
University of Oxford, Oxford, UKTim de Laat
Kiel University, Kiel, GermanyDamian Sawicki
KU Leuven, Leuven, Belgium

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.
Cite this article
Goulnara Arzhantseva, Dawid Kielak, Tim de Laat, Damian Sawicki, Spectral gap and origami expanders. Comment. Math. Helv. (2025), published online first
DOI 10.4171/CMH/589