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arXiv · 1010.0284

Z-Structures on Product Groups

Carrie J. Tirel
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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.

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Carrie J. Tirel. 2010-10-02. Z-Structures on Product Groups. https://doi.org/10.2140/agt.2011.11.2587

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