${\rm CAT(0)}$ cube complexes are determined by their boundary cross ratio
Geometric Topology
2022-01-28 v4 Group Theory
Abstract
We introduce a -valued cross ratio on Roller boundaries of cube complexes. We motivate its relevance by showing that every cross-ratio preserving bijection of Roller boundaries uniquely extends to a cubical isomorphism. Our results are strikingly general and even apply to infinite dimensional, locally infinite cube complexes with trivial automorphism group.
Keywords
Cite
@article{arxiv.1805.08478,
title = {${\rm CAT(0)}$ cube complexes are determined by their boundary cross ratio},
author = {Jonas Beyrer and Elia Fioravanti and Merlin Incerti-Medici},
journal= {arXiv preprint arXiv:1805.08478},
year = {2022}
}
Comments
19 pages, 3 figures. Final version, to appear on Groups Geom Dyn