Spectral gap and origami expanders

  • Goulnara Arzhantseva

    Universität Wien, Wien, Austria
  • Dawid Kielak

    University of Oxford, Oxford, UK
  • Tim de Laat

    Kiel University, Kiel, Germany
  • Damian Sawicki

    KU Leuven, Leuven, Belgium
Spectral gap and origami expanders cover
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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