Abstract This work focuses on important step in quantitative topology: given homotopic mappings from Sm$S^m$ to Sn$S^n$ of Lipschitz constant L$L$, 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$m = 3$, n=2$n = 2$, constructing a homotopy with Lipschitz constant O(L)$O(L)$.
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