Trees of manifolds as boundaries of spaces and groups

Abstract

We show that trees of manifolds, the topological spaces introduced by Jakobsche, appear as boundaries at infinity of various spaces and groups. In particular, they appear as Gromov boundaries of some hyperbolic groups, of arbitrary dimension, obtained by the procedure of strict hyperbolization. We also recognize these spaces as boundaries of arbitrary Coxeter groups with manifold nerves, and as Gromov boundaries of the fundamental groups of singular spaces obtained from some finite volume hyperbolic manifolds by cutting off their cusps and collapsing the resulting boundary tori to points.

23 pages

References in corpus (1)

• Trees of metric compacta and trees of manifolds

Cited by in corpus (8)

• Bowditch's JSJ tree and the quasi-isometry classification of certain Coxeter groups, with an appendix written jointly with Christopher Cashen
• Trees of metric compacta and trees of manifolds
• Special cubulation of strict hyperbolization
• Right-angled Coxeter groups with n-dimensional Sierpiński compacta as boundaries
• Reflection trees of graphs as boundaries of Coxeter groups
• Relative cubulation of relative strict hyperbolization
• Convex cocompact groups in real hyperbolic spaces with limit set a Pontryagin sphere
• Finite-State Machines for Horospheres in Hyperbolic Right-Angled Coxeter Groups