Volume 24, issue 2 (2020)

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Trees of manifolds as boundaries of spaces and groups

Jacek Świątkowski

Geometry & Topology 24 (2020) 593–622

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.

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hyperbolic group, Gromov boundary
Mathematical Subject Classification 2010
Primary: 20F67
Secondary: 20F65, 57M07
Received: 25 April 2013
Revised: 19 January 2016
Accepted: 6 August 2019
Published: 23 September 2020
Proposed: Steve Ferry
Seconded: John Lott, Bruce Kleiner
Jacek Świątkowski
Instytut Matematyczny
Uniwersytet Wrocławski