Spectral gap and origami expanders
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.
Authors
- Dawid Kielak (ORCID: https://orcid.org/0000-0002-5536-9070)
- Tim de Laat (ORCID: https://orcid.org/0000-0002-5659-4026)
- Damian Sawicki (ORCID: https://orcid.org/0000-0002-4977-2509)
- Goulnara Arzhantseva
Institutions
- University of Vienna (AT)
- Christian-Albrechts-Universität zu Kiel (DE)
- University of Oxford (GB)
- Hochschule Campus Wien (AT)
- KU Leuven (BE)
Publication Details
- Journal
- Commentarii Mathematici Helvetici
- Published
- 2025-03-28
- DOI
- https://doi.org/10.4171/cmh/589
- Primary Topic
- Advanced Materials and Mechanics
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Deutsche Forschungsgemeinschaft
- Fonds Wetenschappelijk Onderzoek
- Vlaamse regering
- Mathematisches Forschungsinstitut Oberwolfach