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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 ℰZ–structure. The general questions of which groups admit Z– or ℰZ–structures remain open. Here we show that all Baumslag–Solitar groups admit ℰZ–structures and all generalized Baumslag–Solitar groups admit Z–structures.
Keywords: $\mathcal{Z}$–structure, $\mathcal{Z}$–boundary, group boundaries, Baumslag–Solitar groups, group boundary
Guilbault, Craig 1 ; Moran, Molly 2 ; Tirel, Carrie 3
@article{10_2140_agt_2019_19_2077,
author = {Guilbault, Craig and Moran, Molly and Tirel, Carrie},
title = {Boundaries of {Baumslag{\textendash}Solitar} groups},
journal = {Algebraic and Geometric Topology},
pages = {2077--2097},
publisher = {mathdoc},
volume = {19},
number = {4},
year = {2019},
doi = {10.2140/agt.2019.19.2077},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2019.19.2077/}
}
TY - JOUR AU - Guilbault, Craig AU - Moran, Molly AU - Tirel, Carrie TI - Boundaries of Baumslag–Solitar groups JO - Algebraic and Geometric Topology PY - 2019 SP - 2077 EP - 2097 VL - 19 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2019.19.2077/ DO - 10.2140/agt.2019.19.2077 ID - 10_2140_agt_2019_19_2077 ER -
%0 Journal Article %A Guilbault, Craig %A Moran, Molly %A Tirel, Carrie %T Boundaries of Baumslag–Solitar groups %J Algebraic and Geometric Topology %D 2019 %P 2077-2097 %V 19 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2019.19.2077/ %R 10.2140/agt.2019.19.2077 %F 10_2140_agt_2019_19_2077
Guilbault, Craig; Moran, Molly; Tirel, Carrie. Boundaries of Baumslag–Solitar groups. Algebraic and Geometric Topology, Tome 19 (2019) no. 4, pp. 2077-2097. doi: 10.2140/agt.2019.19.2077
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