Regular finite decomposition complexity Journal Articles

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.

authors

• Kasprowski, Daniel
• Nicas, Andrew John
• Rosenthal, David

status

• published 

publication date

• September 2019

has subject area

• 0101 Pure Mathematics (FoR)

published in

• Journal of Topology and Analysis  Journal

keywords

• Coarse geometry
• K-THEORY
• Mathematics
• Physical Sciences
• Science & Technology
• assembly maps
• asymptotic dimension
• decomposition complexity
• integral Novikov conjecture
• permanence properties

Digital Object Identifier (DOI)

• 10.1142/s1793525319500286

start page

• 691

end page

• 719

volume

• 11

issue

• 03