On boundaries of bicombable spaces
Group Theory
2025-05-13 v2 Metric Geometry
Abstract
We initiate systematic study of EZ-structures (and associated boundaries) of groups acting on spaces that admit consistent and conical (equivalently, consistent and convex) geodesic bicombings. Such spaces recently drew a lot of attention due to the fact that many classical groups act `nicely' on them. We rigorously construct EZ-structures, discuss their uniqueness (up to homeomorphism), provide examples, and prove some boundary-related features analogous to the ones exhibited by CAT(0) spaces and groups, which form a subclass of the discussed class of spaces and groups.
Cite
@article{arxiv.2503.06673,
title = {On boundaries of bicombable spaces},
author = {Daniel Danielski},
journal= {arXiv preprint arXiv:2503.06673},
year = {2025}
}
Comments
Modifications in the Introduction and Remark 2.5 regarding the [Bas24] paper. Section 5 adapted to work under more general assumptions, in view of the [HHP25] paper