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… 
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