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Boundaries of Baumslag-Solitar groups. (English) Zbl 07121521
Summary: 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 \(\mathcal{E}\mathcal{Z}\)-structure. The general questions of which groups admit \(\mathcal{Z}\)- or \(\mathcal{E}\mathcal{Z}\)-structures remain open. Here we show that all Baumslag–Solitar groups admit \(\mathcal{E}\mathcal{Z}\)–structures and all generalized Baumslag-Solitar groups admit \(\mathcal{Z}\)-structures.

MSC:
20F65 Geometric group theory
57M07 Topological methods in group theory
57M60 Group actions on manifolds and cell complexes in low dimensions
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