Spectral gap and origami expanders
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866910342156648448 |
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| author | Arzhantseva, Goulnara Kielak, Dawid de Laat, Tim Sawicki, Damian |
| author_facet | Arzhantseva, Goulnara Kielak, Dawid de Laat, Tim Sawicki, Damian |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2112_11864 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Spectral gap and origami expanders Arzhantseva, Goulnara Kielak, Dawid de Laat, Tim Sawicki, Damian Metric Geometry Dynamical Systems Group Theory Geometric Topology 05C48 (20F65, 37A30, 37E30, 51F30, 57M60) 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. |
| title | Spectral gap and origami expanders |
| topic | Metric Geometry Dynamical Systems Group Theory Geometric Topology 05C48 (20F65, 37A30, 37E30, 51F30, 57M60) |
| url | https://arxiv.org/abs/2112.11864 |