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EMBEDDABILITY OF GENERALISED WREATH PRODUCTS

Part of: Structure and classification of infinite or finite groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  15 December 2014

CHRIS CAVE  and
DENNIS DREESEN
CHRIS CAVE*
Affiliation:
School of Mathematics, University of Southampton, Highfield, Southampton SO17 1BJ, UK email cc1g11@soton.ac.uk
DENNIS DREESEN
Affiliation:
School of Mathematics, University of Southampton, Highfield, Southampton SO17 1BJ, UK email Dennis.Dreesen@soton.ac.uk
*
✉cc1g11@soton.ac.uk
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Abstract

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Given two finitely generated groups that coarsely embed into a Hilbert space, it is known that their wreath product also embeds coarsely into a Hilbert space. We introduce a wreath product construction for general metric spaces $X,Y,Z$ and derive a condition, called the (${\it\delta}$-polynomial) path lifting property, such that coarse embeddability of $X,Y$ and $Z$ implies coarse embeddability of $X\wr _{Z}Y$. We also give bounds on the compression of $X\wr _{Z}Y$ in terms of ${\it\delta}$ and the compressions of $X,Y$ and $Z$.

Keywords

coarse embeddingcompressionwreath products

MSC classification

Primary: 20F65: Geometric group theory
Secondary: 20E22: Extensions, wreath products, and other compositions 20F69: Asymptotic properties of groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 2 , April 2015 , pp. 250 - 263
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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