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math.MG2022★ 2 cited
Degrees of maps and multiscale geometry
Aleksandr Berdnikov, Larry Guth, Fedor Manin
We study the degree of an -Lipschitz map between Riemannian manifolds, proving new upper bounds and constructing new examples. For instance, if is the connected sum of …
math.MG2020
Waist of maps measured via Urysohn width
Alexey Balitskiy, Aleksandr Berdnikov
We discuss various questions of the following kind: for a continuous map from a compact metric space to a simplicial complex, can one guarantee the existence of a fiber l…
math.MG2020★ 3 cited
Local-to-global Urysohn width estimates
Alexey Balitskiy, Aleksandr Berdnikov
The notion of the Urysohn -width measures to what extent a metric space can be approximated by a -dimensional simplicial complex. We investigate how local Urysohn width bound…