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

Carrie J Tirel

Algebraic & Geometric Topology 11 (2011) 2587–2625
Abstract

A Z–structure on a group G, defined by M Bestvina, is a pair (X̂,Z) of spaces such that X̂ is a compact ER, Z is a Z–set in X̂, G acts properly and cocompactly on X = X̂Z and the collection of translates of any compact set in X forms a null sequence in X̂. 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