Lipschitz homotopies of mappings from 3‐sphere to 2‐sphere

Abstract

This work focuses on important step in quantitative topology: given homotopic mappings from 𝑆 𝑚 to 𝑆 𝑛 of Lipschitz constant 𝐿, build the (asymptotically) simplest homotopy between them (meaning having the least Lipschitz constant). The present paper resolves this problem for the first case where Hopf invariant plays a role: 𝑚 = 3, 𝑛 = 2, constructing a homotopy with Lipschitz constant 𝑂(𝐿).M S C 2 0 2 0 51H20 (primary), 57M50 (secondary)