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Lipschitz homotopies of mappings from 3-sphere to 2-sphere
Journal of Topology ( IF 0.8 ) Pub Date : 2022-06-11 , DOI: 10.1112/topo.12239
Aleksandr Berdnikov 1
Affiliation  

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:

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 小号 $S^m$ 小号 n $S^n$ Lipschitz 常数 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: = 3 $m = 3$ , n = 2 $n = 2$ , 用 Lipschitz 常数构造同伦 ( 大号 ) $O(L)$ .
更新日期:2022-06-13
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