Straightening warped cones
Published 2017-05-18Version 1
We provide converses to two results of J. Roe (Geom. Topol. 2005): first, the warped cone over a free action of a Haagerup group admits a fibred coarse embedding into a Hilbert space, and second, a free action yielding a warped cone with property A must be amenable. We construct examples showing that in both cases the freeness assumption is necessary. The first equivalence is obtained also for other classes of Banach spaces, e.g. for $L^p$-spaces.