Year: 2025
Type: article
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.
DOI: 10.4171/cmh/589
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Awards: G1399780489, G1652504919, Von Neumann algebras, ergodic theory and boundary actions, SFB 1442: Geometrie: Deformationen und Rigidität, EXC 2044: Mathematik Münster: Dynamik – Geometrie – Struktur, G6938060324, ANALYTIC PROPERTIES OF INFINITE GROUPS:limits, curvature, and randomness, Fibring of manifolds and groups
OpenAlex ID: W4408941986