Super-expanders and warped cones

Sawicki, Damian

doi:10.5802/aif.3373

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Super-expanders and warped cones

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Sawicki, Damian
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.5802/aif.3373
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Citation

Sawicki, D. (2020). Super-expanders and warped cones. Annales de l'Institut Fourier, 70(4), 1753-1774. doi:10.5802/aif.3373.

Cite as: https://hdl.handle.net/21.11116/0000-0008-B73A-9

Abstract

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