Straightening warped cones

Damian Sawicki; Jianchao Wu

doi:10.1142/s179352532050034x

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arXiv · 1705.06725

Straightening warped cones

Damian Sawicki·Jianchao Wu

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Abstract

We provide the converses to two results of J. Roe (Geom. Topol. 2005): first, the warped cone associated to a free action of an a-T-menable 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, in particular for $L^p$-spaces.

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Damian Sawicki, Jianchao Wu. 2020-02-04. Straightening warped cones. https://doi.org/10.1142/s179352532050034x

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