Asymptotic cones and Assouad-Nagata dimension

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We prove the dimension of any asymptotic cone over a metric space X does not exceed the asymptotic Assouad-Nagata dimension of X. This improves a result of Dranishnikov and Smith who showed that dim(Y) does not exceed asymptotic Assouad-Nagata dimension of X for all separable subsets Y of special asymptotic cones of X over an exponential ultrafilter. We also show that Assouad-Nagata dimension of the discrete Heisenberg group equals its asymptotic dimension.
11 pages, comments from Behrstock, Brodskiy, Dranishnikov included

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Metric Geometry, Geometric Topology

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http://salesiana.dossiersoluciones.com/handle/123456789/210575

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0610338
 http://arxiv.org/abs/math/0610338
 Proceedings of the American Math.Soc. 136 (2008), 2225--2233

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