Compression bounds for wreath products

2009/07/29 by Li, Sean
#FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.0907.5017

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=\Z, H=\Z \wr \Z our result implies that the Hilbert compression exponent of \Z\wr (\Z\wr\Z) is at least 1/4, answering a question posed as to whether it has positive Hilbert compression exponent.

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