Trees of metric compacta and trees of manifolds

Świątkowski, Jacek

doi:10.2140/gt.2020.24.533

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Trees of metric compacta and trees of manifolds

Jacek Świątkowski

Geometry & Topology 24 (2020) 533–592

DOI: 10.2140/gt.2020.24.533

Abstract

We present a construction, called a tree of spaces, that allows us to produce many compact metric spaces that are good candidates for being (up to homeomorphism) Gromov boundaries of some hyperbolic groups. We develop also a technique that allows us (1) to work effectively with the spaces in this class and (2) to recognize ideal boundaries of various classes of infinite groups, up to homeomorphism, as some spaces in this class.

We illustrate the effectiveness of the presented technique by clarifying, correcting and extending various results concerning the already widely studied class of spaces called trees of manifolds.

In a companion paper (Geom. Topol. 24 (2020) 593–622), which builds upon results from the present paper, we show that trees of manifolds in arbitrary dimension appear as Gromov boundaries of some hyperbolic groups.

Keywords

compact metric space, inverse limit, ideal boundary

Mathematical Subject Classification 2010

Primary: 20F65

Secondary: 57M07, 54D80

References

Publication

Received: 25 April 2013

Revised: 3 January 2019

Accepted: 6 August 2019

Published: 23 September 2020

Proposed: Steve Ferry

Seconded: Bruce Kleiner, Martin Bridson

Authors

Jacek Świątkowski
Instytut Matematyczny Uniwersytet Wrocławski Wrocław Poland

Volume 24, issue 2 (2020)