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Asymptotic dimension, property A, and Lipschitz maps

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Abstract

It is well-known that a paracompact space X is of covering dimension n if and only if any map f:X→K from X to a simplicial complex K can be pushed into its n-skeleton K (n). We use the same idea to define dimension in the coarse category. It turns out the analog of maps f:X→K is related to asymptotically Lipschitz maps, the analog of paracompact spaces are spaces related to Yu’s Property A, and the dimension coincides with Gromov’s asymptotic dimension.

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Acknowledgements

This research was supported by the Slovenian Research Agency grants P1-0292-0101 and J1-2057-0101. The second-named author was partially supported by MEC, MTM2006-0825.

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Authors and Affiliations

  1. Pedagoška Fakulteta in IMFM, Univerza v Ljubljani, Jadranska ulica 19, 1111, Ljubljana, Slovenia

    M. Cencelj

  2. University of Tennessee, Knoxville, TN, 37996, USA

    J. Dydak

  3. Fakulteta za Matematiko in Fiziko, Univerza v Ljubljani, Jadranska ulica 19, 1111, Ljubljana, Slovenia

    A. Vavpetič

Authors
  1. M. Cencelj
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  2. J. Dydak
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  3. A. Vavpetič
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Correspondence to A. Vavpetič.

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Cencelj, M., Dydak, J. & Vavpetič, A. Asymptotic dimension, property A, and Lipschitz maps. Rev Mat Complut 26, 561–571 (2013). https://doi.org/10.1007/s13163-012-0102-2

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  • DOI: https://doi.org/10.1007/s13163-012-0102-2

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