Linear nullhomotopies for maps to spheres

Abstract: I will explain the following theorem. Let $X$ be a finite complex ($S^m$ is a good example to keep in mind). Then every nullhomotopic, $L$-Lipschitz map $X \to S^n$ has a $C(X,n) \cdot (L+1)$-Lipschitz nullhomotopy. The proof is spread over several papers, and the full story has never been told in one place. Joint and separate work variously with Chambers, Dotterrer, Weinberger, Berdnikov, and Guth.

differential geometrygeometric topologymetric geometry

Audience: researchers in the topic

Topology and geometry: extremal and typical

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