Distortion of imbeddings of groups of intermediate growth into metric spaces

Laurent Bartholdi, Anna G. Erschler

Published 2014-06-23, updated 2014-06-25Version 2

For every metric space $\mathcal X$ in which there exists a sequence of finite groups of bounded-size generating set that does not embed coarsely, and for every unbounded, increasing function $\rho$, we produce a group of subexponential word growth all of whose imbeddings in $\mathcal X$ have distortion worse than $\rho$. This applies in particular to any B-convex Banach space $\mathcal X$, such as Hilbert space.