Z-Structures on Product Groups
Geometric Topology
2016-01-20 v1 Group Theory
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 will show that if two groups each admit a Z-structure, then so do their free and direct products.
Keywords
Cite
@article{arxiv.1010.0284,
title = {Z-Structures on Product Groups},
author = {Carrie J. Tirel},
journal= {arXiv preprint arXiv:1010.0284},
year = {2016}
}