Roller boundaries for median spaces and algebras

Fioravanti, Elia

doi:10.2140/agt.2020.20.1325

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Roller boundaries for median spaces and algebras

Elia Fioravanti

Algebraic & Geometric Topology 20 (2020) 1325–1370

DOI: 10.2140/agt.2020.20.1325

Abstract

We construct compactifications for median spaces with compact intervals, generalising Roller boundaries of $CAT (0)$ cube complexes. Examples of median spaces with compact intervals include all finite-rank median spaces and all proper median spaces of infinite rank. Our methods also apply to general median algebras, where we recover the zero-completions of Bandelt and Meletiou (1993). Along the way, we prove various properties of halfspaces in finite-rank median spaces and a duality result for locally convex median spaces.

Keywords

median space, median algebra, horofunction compactification, Roller boundary, spaces with walls

Mathematical Subject Classification 2010

Primary: 20F65

Secondary: 20F67, 22F50, 51F99, 57M99

References

Publication

Received: 25 August 2018

Revised: 24 May 2019

Accepted: 26 August 2019

Published: 27 May 2020

Authors

Elia Fioravanti
Mathematical Institute University of Oxford Oxford United Kingdom

Volume 20, issue 3 (2020)