Finite asymptotic dimension for CAT(0) cube complexes
We prove that the asymptotic dimension of a finite-dimensional CAT(0) cube complex is bounded above by the dimension. To achieve this we prove a controlled colouring theorem for the complex. We also show that every CAT(0) cube complex is a contractive retraction of an infinite dimensional cube. As a...
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| Format: | Article |
| Language: | English |
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2012-04-08.
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| Online Access: | Get fulltext Get fulltext |
| Summary: | We prove that the asymptotic dimension of a finite-dimensional CAT(0) cube complex is bounded above by the dimension. To achieve this we prove a controlled colouring theorem for the complex. We also show that every CAT(0) cube complex is a contractive retraction of an infinite dimensional cube. As an example of the dimension theorem we obtain bounds on the asymptotic dimension of small cancellation groups. |
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