Roller boundaries for median spaces and algebras

Fioravanti, Elia¹

¹Mathematical Institute, University of Oxford, Oxford, United Kingdom

Algebraic and Geometric Topology, Tome 20 (2020) no. 3, pp. 1325-1370

Résumé

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.

Détail

DOI : 10.2140/agt.2020.20.1325

Classification : 20F65, 20F67, 22F50, 51F99, 57M99
Keywords: median space, median algebra, horofunction compactification, Roller boundary, spaces with walls

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