Roller boundaries for median spaces and algebras
Metric Geometry
2021-09-27 v4 Geometric Topology
Abstract
We construct compactifications for median spaces with compact intervals, generalising Roller boundaries of 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 work for general median algebras, where we recover the zero-completions of Bandelt and Meletiou. Along the way, we prove various properties of halfspaces in finite rank median spaces and a duality result for locally convex median spaces.
Cite
@article{arxiv.1708.01005,
title = {Roller boundaries for median spaces and algebras},
author = {Elia Fioravanti},
journal= {arXiv preprint arXiv:1708.01005},
year = {2021}
}
Comments
39 pages, 3 figures. Compared to published version, corrected Figure 1 (needed in an example). Many thanks to Mark Hagen for spotting this