Compression bounds for wreath products

Abstract

We show that if $G$ and $H$ are finitely generated groups whose Hilbert compression exponent is positive, then so is the Hilbert compression exponent of the wreath $G\wr H$. We also prove an analogous result for coarse embeddings of wreath products. In the special case $G=\mathbb{Z}$, $H=\mathbb{Z}\wr \mathbb{Z}$ our result implies that the Hilbert compression exponent of $\mathbb{Z}\wr (\mathbb{Z}\wr \mathbb{Z})$ is at least 1/4, answering a question posed as to whether it has positive Hilbert compression exponent.

12 pages, version to appear in Proc. Amer. Math. Soc

References in corpus (3)

• $L_p$ compression, traveling salesmen, and stable walks
• The wreath product of Z with Z has Hilbert compression exponent 2/3
• Proper actions of wreath products and generalizations