Regular finite decomposition complexity
Regular finite decomposition complexity
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.
Coarse geometry, assembly maps, asymptotic dimension, decomposition complexity, integral Novikov conjecture, permanence properties
691-719
Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075
Nicas, Andrew
4b03e3ce-b9cc-4a7b-879e-cd448c2f20dc
Rosenthal, David
220af846-9bc6-4450-bd5c-35b4f361d387
25 January 2018
Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075
Nicas, Andrew
4b03e3ce-b9cc-4a7b-879e-cd448c2f20dc
Rosenthal, David
220af846-9bc6-4450-bd5c-35b4f361d387
Kasprowski, Daniel, Nicas, Andrew and Rosenthal, David
(2018)
Regular finite decomposition complexity.
Journal of Topology and Analysis, 11 (3), .
(doi:10.1142/S1793525319500286).
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.
This record has no associated files available for download.
More information
Accepted/In Press date: 5 December 2017
Published date: 25 January 2018
Keywords:
Coarse geometry, assembly maps, asymptotic dimension, decomposition complexity, integral Novikov conjecture, permanence properties
Identifiers
Local EPrints ID: 478537
URI: http://eprints.soton.ac.uk/id/eprint/478537
ISSN: 1793-5253
PURE UUID: 454e80c3-5546-4b32-bc90-692acf79071f
Catalogue record
Date deposited: 04 Jul 2023 17:48
Last modified: 17 Mar 2024 04:19
Export record
Altmetrics
Contributors
Author:
Daniel Kasprowski
Author:
Andrew Nicas
Author:
David Rosenthal
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics