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

Aleksandr Berdnikov

doi:10.1112/topo.12239

paper

Lipschitz null-homotopy of mappings $S^{3} \to S^{2}$

arXiv:1811.02606 · doi:10.1112/topo.12239

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 $O (L)$

27 pages, 20 figures

Lipschitz null-homotopy of mappings S3→S2

Abstract

References in corpus (3)

Lipschitz null-homotopy of mappings $S^{3} \to S^{2}$