Surveys in Differential Geometry

Volume 22 (2017)

Recent progress in quantitative topology

Pages: 191 – 216

DOI: http://dx.doi.org/10.4310/SDG.2017.v22.n1.a7

Author

Larry Guth (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.)

Abstract

We discuss recent work of Chambers, Dotterrer, Ferry, Manin, and Weinberger, which resolved a fundamental question in quantitative topology: if $f : S^m \to S^n$ is a contractible map with Lipschitz constant $L$, what can we say about the Lipschitz constant of a nullhomotopy of $f$?

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Published 13 September 2018