Document Type

Article

Publication Date

1-1-2022

Abstract

Bestvina introduced a Z-structure for a group G to generalize the boundary of a CAT(0) or hyperbolic group. A refinement of this notion, introduced by Farrell and Lafont, includes a G-equivariance requirement, and is known as an ξZ-structure. A recent result of the first two authors with Tirel put ξZ-structures on Baumslag–Solitar groups and Z-structures on generalized Baumslag–Solitar groups. We generalize this to higher dimensions by showing that fundamental groups of graphs of closed nonpositively curved Riemannian n-manifolds (each vertex and edge manifold is of dimension n) admit Z-structures, and graphs of negatively curved or flat Riemannian n-manifolds admit ξZ-structures.

Publication Source (Journal or Book title)

Fundamenta Mathematicae

First Page

47

Last Page

75

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