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Boundaries of Baumslag–Solitar groups

Craig R Guilbault, Molly A Moran and Carrie J Tirel

Algebraic & Geometric Topology 19 (2019) 2077–2097

A 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 Z–structure. The general questions of which groups admit Z– or Z–structures remain open. Here we show that all Baumslag–Solitar groups admit Z–structures and all generalized Baumslag–Solitar groups admit Z–structures.

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$\mathcal{Z}$–structure, $\mathcal{Z}$–boundary, group boundaries, Baumslag–Solitar groups, group boundary
Mathematical Subject Classification 2010
Primary: 20F65, 57M07, 57M60
Received: 23 August 2018
Revised: 28 November 2018
Accepted: 20 December 2018
Published: 16 August 2019
Craig R Guilbault
Department of Mathematical Sciences
University of Wisconsin - Milwaukee
Milwaukee, WI
United States
Molly A Moran
Department of Mathematics
The Colorado College
Colorado Springs
Colorado United States
Carrie J Tirel
Department of Mathematics
University of Wisconsin - Fox Valley
Menasha, WI
United States