zbMATH — the first resource for mathematics

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
Full Text:
References:
 [1] 10.1112/jlms/jdq091 · Zbl 1235.54017 [2] 10.1023/A:1007755408585 · Zbl 0932.46063 [3] 10.1307/mmj/1029005393 · Zbl 0872.57005 [4] 10.2307/2939264 · Zbl 0767.20014 [5] 10.1007/978-3-662-12494-9 [6] 10.1112/S0024611502013989 · Zbl 1031.20039 [7] 10.1090/conm/394/07435 [8] 10.4171/CMH/7 · Zbl 1094.57003 [9] 10.1007/978-1-4613-9730-4_9 [10] 10.1016/j.exmath.2018.03.004 [11] 10.2140/gt.2014.18.31 · Zbl 1315.20041 [12] 10.4064/cm111-1-8 · Zbl 1140.20033 [13] ; Meintrup, New York J. Math., 8, 1, (2002) [14] 10.2140/gt.2009.13.2807 · Zbl 1271.20056 [15] 10.2140/agt.2011.11.2587 · Zbl 1232.57002 [16] 10.1007/s00039-001-8232-6 · Zbl 1004.20024 [17] 10.2307/121011 · Zbl 0911.19001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.