Regular finite decomposition complexity

Kasprowski, Daniel; Nicas, Andrew; Rosenthal, David

doi:10.1142/S1793525319500286

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Regular finite decomposition complexity

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Kasprowski, Daniel
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1142/S1793525319500286
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arXiv:1608.04516.pdf
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Citation

Kasprowski, D., Nicas, A., & Rosenthal, D. (2019). Regular finite decomposition complexity. Journal of Topology and Analysis, 11(3), 691-719. doi:10.1142/S1793525319500286.

Cite as: https://hdl.handle.net/21.11116/0000-0004-A67F-3

Abstract

We introduce the notion of regular finite decomposition complexity of a metric family. This generalizes Gromov's finite asymptotic dimension and is motivated by the concept of finite decomposition complexity (FDC) due to
Guentner, Tessera and Yu. Regular finite decomposition complexity implies FDC and has all the permanence properties that are known for FDC, as well as a new one called Finite Quotient Permanence. We show that for a collection containing all metric families with finite asymptotic dimension all other permanence properties follow from Fibering Permanence.