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arXiv · 2112.11864

Spectral gap and origami expanders

Goulnara Arzhantseva·Dawid Kielak·Tim de Laat·Damian Sawicki
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Abstract

We construct the first measure-preserving affine actions with spectral gap on surfaces of arbitrary genus $g > 1$. 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.

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Goulnara Arzhantseva, Dawid Kielak, Tim de Laat, Damian Sawicki. 2024-02-26. Spectral gap and origami expanders. https://arxiv.org/abs/2112.11864

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