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

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arxiv 1811.02606 v3 pith:OAXHBJGV submitted 2018-11-06 math.GT

Aleksandr Berdnikov This is my paper · ORCID
classification math.GT
keywords lipschitzconstanthomotopymappingsasymptoticallybuildcaseconstructing
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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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  1. A hardness of approximation result in metric geometry

    math.DG 2019-08 accept novelty 8.0 of 10

    It is NP-hard to approximate the hyperspherical radius of triangulated surfaces and triangulated high-dimensional spheres to within any almost-polynomial factor.

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