CAT(0) cube complexes are determined by their boundary cross ratio (Q2035117)
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scientific article; zbMATH DE number 7362830
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | CAT(0) cube complexes are determined by their boundary cross ratio |
scientific article; zbMATH DE number 7362830 |
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CAT(0) cube complexes are determined by their boundary cross ratio (English)
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24 June 2021
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Summary: We introduce a \(\mathbb{Z}\)-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.
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CAT(0) cube complexes
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cross ratios
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Roller boundary
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