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

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Abstract:

We introduce a \Z–valued cross ratio on Roller boundaries of \mathrmCAT 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.

SEEK ID: https://publications.h-its.org/publications/991

Research Groups: Groups and Geometry

Publication type: Misc

Journal: (to appear in Groups, Geometry and Dynamics)

Citation: arXiv,math.GT,1805.08478

Date Published: 2018

URL: https://arxiv.org/abs/1805.08478

Registered Mode: imported from a bibtex file

Authors: Jonas Beyrer, Elia Fioravanti, Merlin Incerti-Medici

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