Warped cones and spectral gaps

Abstract

We show that warped cones over actions with spectral gaps do not embed coarsely into large classes of Banach spaces. In particular, there exist warped cones over actions of the free group that do not embed coarsely into $L_p$-spaces and there are warped cones over discrete group actions that do not embed into any Banach space with non-trivial type.

7 pages; final version, to appear in PAMS

References in corpus (2)

• Averaged projections, angles between groups and strengthening of property (T)
• A spectral gap theorem in simple Lie groups

Cited by in corpus (9)

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• Superexpanders from group actions on compact manifolds
• Warped cones, (non-)rigidity, and piecewise properties, with a joint appendix with Dawid Kielak
• Straightening warped cones
• Logarithmic girth expander graphs of $S{L}_n({\mathbb{F}}_p)$
• A Markovian and Roe-algebraic approach to asymptotic expansion in measure
• Warped cones and proper affine isometric actions of discrete groups on Banach spaces
• Rigidity of warped cones and coarse geometry of expanders
• Amenability versus non-exactness of dense subgroups of a compact group