English

Super-expanders and warped cones

Metric Geometry 2021-04-21 v2 Dynamical Systems Functional Analysis Group Theory

Abstract

For a Banach space XX, we show that any family of graphs quasi-isometric to levels of a warped cone OΓY\mathcal O_\Gamma Y is an expander with respect to XX if and only if the induced Γ\Gamma-representation on L2(Y;X)L^2(Y;X) has a spectral gap. This provides examples of graphs that are an expander with respect to all Banach spaces of non-trivial type.

Keywords

Cite

@article{arxiv.1704.03865,
  title  = {Super-expanders and warped cones},
  author = {Damian Sawicki},
  journal= {arXiv preprint arXiv:1704.03865},
  year   = {2021}
}

Comments

15 pages; to appear in Ann. Inst. Fourier; exposition rewritten, main result slightly generalised to accommodate local spectral gaps

R2 v1 2026-06-22T19:15:58.937Z