Distortion in loop space

Abstract: How efficiently can we represent a large integer multiple $k\alpha$ of a given non-torsion element $\alpha$ of a homotopy group of a Riemannian manifold? Here efficiency is measured by the Lipschitz constant $L$ of a representing map, and the question is quantitatively answered by bounding the asymptotics of the minimal $L$ needed to represent $k\alpha$. In this talk I will talk about related functions defined in terms of the (co)homology of the loop space of the Riemannian manifold. I will discuss results for producing general upper bounds and applications of these, as well as specific constructions for lower bounds.

differential geometrygeometric topologymetric geometry

Audience: researchers in the topic

Topology and geometry: extremal and typical

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