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Preserving coarse properties

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Abstract

The aim of this paper is to investigate properties preserved and co-preserved by coarsely n-to-1 functions, in particular by the quotient maps \(X\rightarrow X/\sim \) induced by a finite group G acting by isometries on a metric space X. The coarse properties we are mainly interested in are related to asymptotic dimension and its generalizations: having finite asymptotic dimension, asymptotic Property C (as defined by Dranishnikov in Rus. Math. Surv. 55(6):1085–1129, 2000), straight finite decomposition complexity, countable asymptotic dimension, and metric sparsification property. We provide an alternative description of asymptotic Property C and we prove that the class of spaces with straight finite decomposition complexity coincides with the class of spaces of countable asymptotic dimension.

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Authors and Affiliations

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

    J. Dydak

  2. Univerza v Ljubljani, Jadranska ulica 19, 1111, Ljubljana, Slovenia

    Ž. Virk

Authors
  1. J. Dydak
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  2. Ž. Virk
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Correspondence to Ž. Virk.

Additional information

The second author was supported by the Slovenian Research Agency grants P1-0292-0101, J1-5435-0101 and J1-6721-0101. The authors would like to thank the referees for useful comments.

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Dydak, J., Virk, Ž. Preserving coarse properties. Rev Mat Complut 29, 191–206 (2016). https://doi.org/10.1007/s13163-015-0182-x

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  • DOI: https://doi.org/10.1007/s13163-015-0182-x

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