Geodesic
CAT(0) cube complexes are determined by their boundary cross ratio
Jonas Beyrer1 orcid ; Elia Fioravanti2 ; Merlin Incerti-Medici1
1Institut des Hautes Études Scientifiques (IHÉS), Bures-sur-Yvette, France
2Universität Bonn, Germany
Groups, geometry, and dynamics, Tome 15 (2021) no. 1, pp. 313-333

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DOI

We introduce a 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.
DOI : 10.4171/ggd/599
Classification : 20-XX, 51-XX, 53-XX
Mots-clés : CAT(0) cube complexes, cross ratios, Roller boundary

Jonas Beyrer  1   ; Elia Fioravanti  2   ; Merlin Incerti-Medici  1

1 Institut des Hautes Études Scientifiques (IHÉS), Bures-sur-Yvette, France
2 Universität Bonn, Germany 
Jonas Beyrer; Elia Fioravanti; Merlin Incerti-Medici. CAT(0) cube complexes are determined by their boundary cross ratio. Groups, geometry, and dynamics, Tome 15 (2021) no. 1, pp. 313-333. doi: 10.4171/ggd/599
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     year = {2021},
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