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Mathematics, Metric Geometry, Dynamical Systems, Group Theory
Abstract:
We provide the converses to two results of Roe [Warped cones and property A, Geom.
Topol. 9 (2005) 163–178, doi:10.2140/9t.2005.9.163]: first, the warped cone associated
to a free action of an a-T-menable group admits a fibered 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, in particular for $L^p$-spaces.
