𝒵–Structures on product groups

Tirel, Carrie J

doi:10.2140/agt.2011.11.2587

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$\mathcal{Z}$–Structures on product groups

Carrie J Tirel

Algebraic & Geometric Topology 11 (2011) 2587–2625

DOI: 10.2140/agt.2011.11.2587

Abstract

A $Z$ –structure on a group $G$ , defined by M Bestvina, is a pair $(\hat{X}, Z)$ of spaces such that $\hat{X}$ is a compact ER, $Z$ is a $Z$ –set in $\hat{X}$ , $G$ acts properly and cocompactly on $X = \hat{X} ∖ Z$ and the collection of translates of any compact set in $X$ forms a null sequence in $\hat{X}$ . It is natural to ask whether a given group admits a $Z$ –structure. In this paper, we show that if two groups each admit a $Z$ –structure, then so do their free and direct products.

Keywords

$\mathcal{Z}$–structure, boundary, free product, direct product, product group

Mathematical Subject Classification 2010

Primary: 57M07

Secondary: 20F65

References

Publication

Received: 14 October 2010

Accepted: 24 June 2011

Published: 16 September 2011

Authors

Carrie J Tirel
Department of Mathematics University of Wisconsin - Fox Valley 1478 Midway Rd Menasha WI 54952 USA

Volume 11, issue 5 (2011)