Trees of manifolds as boundaries of spaces and groups

Świątkowski, Jacek

doi:10.2140/gt.2020.24.593

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Trees of manifolds as boundaries of spaces and groups

Jacek Świątkowski

Geometry & Topology 24 (2020) 593–622

DOI: 10.2140/gt.2020.24.593

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.

Keywords

hyperbolic group, Gromov boundary

Mathematical Subject Classification 2010

Primary: 20F67

Secondary: 20F65, 57M07

References

Publication

Received: 25 April 2013

Revised: 19 January 2016

Accepted: 6 August 2019

Published: 23 September 2020

Proposed: Steve Ferry

Seconded: John Lott, Bruce Kleiner

Authors

Jacek Świątkowski
Instytut Matematyczny Uniwersytet Wrocławski Wrocław Poland

Volume 24, issue 2 (2020)