Regular finite decomposition complexity-Reference-Cited by-同舟云学术

Regular finite decomposition complexity

Published:2019-09 Issue:03 Volume:11 Page:691-719
ISSN:1793-5253
Container-title:Journal of Topology and Analysis
language:en
Short-container-title:J. Topol. Anal.

Author:

Kasprowski Daniel¹^ORCID,Nicas Andrew²,Rosenthal David³

Affiliation:

1. Rheinische Friedrich-Wilhelms-Universität Bonn Mathematisches Institut, Endenicher Allee 60, 53115 Bonn, Germany

2. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1

3. Department of Mathematics and Computer Science, St. John’s University, 8000 Utopia Pkwy, Queens, NY 11439, USA

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Geometry and Topology,Analysis

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793525319500286

Reference11 articles.

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3. A Hurewicz theorem for the Assouad-Nagata dimension

4. A notion of geometric complexity and its application to topological rigidity

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