JournalsggdVol. 15, No. 1pp. 313–333

CAT(0) cube complexes are determined by their boundary cross ratio

  • Jonas Beyrer

    Institut des Hautes Études Scientifiques (IHÉS), Bures-sur-Yvette, France
  • Elia Fioravanti

    Universität Bonn, Germany
  • Merlin Incerti-Medici

    Institut des Hautes Études Scientifiques (IHÉS), Bures-sur-Yvette, France
CAT(0) cube complexes are determined by their boundary cross ratio cover
Download PDF

This article is published open access under our Subscribe to Open model.

Abstract

We introduce a Z\mathbb{Z}-valued cross ratio on Roller boundaries of CAT(0) 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.

Cite this article

Jonas Beyrer, Elia Fioravanti, Merlin Incerti-Medici, CAT(0) cube complexes are determined by their boundary cross ratio. Groups Geom. Dyn. 15 (2021), no. 1, pp. 313–333

DOI 10.4171/GGD/599