Lipschitz null-homotopy of mappings $S^3 \rightarrow S^2$

Aleksandr Berdnikov

doi:10.1112/topo.12239

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arXiv · 1811.02606

Lipschitz null-homotopy of mappings $S^3 \rightarrow S^2$

Aleksandr Berdnikov

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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 $O(L)$

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BibTeX RIS

Aleksandr Berdnikov. 2022-04-03. Lipschitz null-homotopy of mappings $S^3 \rightarrow S^2$. https://doi.org/10.1112/topo.12239

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