Boundaries of Baumslag-Solitar Groups

Craig R. Guilbault; Molly A. Moran; Carrie J. Tirel

doi:10.2140/agt.2019.19.2077

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arXiv · 1808.07923

Boundaries of Baumslag-Solitar Groups

Craig R. Guilbault·Molly A. Moran·Carrie J. Tirel

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Abstract

A $\mathcal{Z}$-structure on a group $G$ was introduced by Bestvina in order to extend the notion of a group boundary beyond the realm of CAT(0) and hyperbolic groups. A refinement of this notion, introduced by Farrell and Lafont, includes a $G$-equivariance requirement, and is known as an $\mathcal{EZ}$-structure. The general questions of which groups admit $\mathcal{Z}$- or $\mathcal{EZ}$-structures remain open. In this paper we add to the current knowledge by showing that all Baumslag-Solitar groups admit $\mathcal{EZ}$-structures and all generalized Baumslag-Solitar groups admit $\mathcal{Z}$-structures.

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Craig R. Guilbault, Molly A. Moran, Carrie J. Tirel. 2018-08-23. Boundaries of Baumslag-Solitar Groups. https://doi.org/10.2140/agt.2019.19.2077

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