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Assouad-Nagata dimension via Lipschitz extensions

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Abstract

In the first part of the paper we show how to relate several dimension theories (asymptotic dimension with Higson property, asymptotic dimension of Gromov and capacity dimension of Buyalo [7]) to Assouad-Nagata dimension. This is done by applying two functors on the Lipschitz category of metric spaces: microscopic and macroscopic. In the second part we identify (among spaces of finite Assouad-Nagata dimension) spaces of Assouad-Nagata dimension at most n as those for which the n-sphere S n is a Lipschitz extensor. Large scale and small scale analogues of that result are given.

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Authors and Affiliations

  1. Department of Mathematics, University of Tennessee, Knoxville, TN, 37996, USA

    N. Brodskiy & J. Dydak

  2. Departamento de Geometría y Topología, Facultad de CC. Matemáticas, Universidad Complutense de Madrid, Madrid, 28040, Spain

    J. Higes

  3. Department of Mathematics, University of Tennessee, Knoxville, TN, 37996, USA

    A. Mitra

Authors
  1. N. Brodskiy
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  2. J. Dydak
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  3. J. Higes
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  4. A. Mitra
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Corresponding author

Correspondence to N. Brodskiy.

Additional information

The author was partially supported by Grant No.2004047 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel.

The author was supported by Grant AP2004-2494 from the Ministerio de Educacion y Ciencia, Spain. He thanks the Department of Mathematics of University of Tennessee for their hospitality.

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Brodskiy, N., Dydak, J., Higes, J. et al. Assouad-Nagata dimension via Lipschitz extensions. Isr. J. Math. 171, 405–423 (2009). https://doi.org/10.1007/s11856-009-0056-3

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  • DOI: https://doi.org/10.1007/s11856-009-0056-3

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