Local-to-global Urysohn width estimates
Name
10.1515_crelle-2021-0047.pdf
Size
2.29 MB
Format
Adobe PDF
Checksum (MD5)
462413ac6342c24c8b68c8367886ee13
Author(s)
Alexey Balitskiy
Aleksandr Berdnikov
Date Issued
August 25, 2021
Journal
Journal für die reine und angewandte Mathematik (Crelles Journal)
Publisher
Walter de Gruyter GmbH
Citation
Balitskiy, Alexey and Berdnikov, Aleksandr. "Local-to-global Urysohn width estimates" Journal für die reine und angewandte Mathematik (Crelles Journal), vol. 2021, no. 780, 2021, pp. 265-274.
Version
Final published version
Abstract
The notion of the Urysohn d-width measures to what extent a metric space can be approximated by a d-dimensional simplicial complex. We investigate how local Urysohn width bounds on a Riemannian manifold affect its global width. We bound the 1-width of a Riemannian manifold in terms of its first homology and the supremal width of its unit balls. Answering a question of Larry Guth, we give examples of n-manifolds of considerable (𝑛−1)-width in which all unit balls have arbitrarily small 1-width. We also give examples of topologically simple manifolds that are locally nearly low-dimensional.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1515/crelle-2021-0047
