Regular Finite Decomposition Complexity
Metric Geometry
2020-01-22 v2 Algebraic Topology
Geometric Topology
K-Theory and Homology
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.
Cite
@article{arxiv.1608.04516,
title = {Regular Finite Decomposition Complexity},
author = {Daniel Kasprowski and Andrew Nicas and David Rosenthal},
journal= {arXiv preprint arXiv:1608.04516},
year = {2020}
}
Comments
29 pages. Final version, containing several minor improvements. To appear in the Journal of Topology and Analysis