This work focuses on important step in quantitative topology: given homotopic mappings from $S^m$$S^m$ to $S^n$$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)$.

中文翻译：

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从 3-sphere 到 2-sphere 映射的 Lipschitz 同伦

这项工作的重点是定量拓扑中的重要步骤：给定同伦映射${\mathrm{小号}}^{米}$$S^m$至${\mathrm{小号}}^n$$S^n$Lipschitz 常数$\mathrm{大号}$$L$，在它们之间建立（渐近）最简单的同伦（意味着具有最小的 Lipschitz 常数）。本文针对 Hopf 不变量起作用的第一种情况解决了这个问题：$米=3$$m=3$,$n=2$$n=2$, 用 Lipschitz 常数构造同伦$○(\mathrm{大号})$$O(L)$.