# Local-to-global Urysohn width estimates

@article{Balitskiy2020LocaltoglobalUW, title={Local-to-global Urysohn width estimates}, author={Alexey Balitskiy and Aleksandr Berdnikov}, journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)}, year={2020}, volume={2021}, pages={265 - 274} }

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){(n-1)}-width in which all unit balls have arbitrarily…

## 2 Citations

### Macroscopic scalar curvature and codimension 2 width

- Mathematics
- 2021

We show that a complete 3-dimensional Riemannian manifold M with finitely generated first homology has macroscopic dimension 1 if it satisfies the following “macroscopic curvature” assumptions: every…

### Waist of maps measured via Urysohn width

- Mathematics
- 2020

We discuss various questions of the following kind: for a continuous map $X \to Y$ from a compact metric space to a simplicial complex, can one guarantee the existence of a fiber large in the sense…

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