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 |
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| 100 | 1 | 0 | |a Wright, Nick |e author |
| 245 | 0 | 0 | |a Finite asymptotic dimension for CAT(0) cube complexes |
| 260 | |c 2012-04-08. | ||
| 856 | |z Get fulltext |u https://eprints.soton.ac.uk/147377/1/1004.4172v1 | ||
| 856 | |z Get fulltext |u https://eprints.soton.ac.uk/147377/2/1004.4172v1 | ||
| 520 | |a 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. | ||
| 655 | 7 | |a Article | |