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arXiv · 2008.10761

Filling random cycles

Fedor Manin
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Abstract

We compute the asymptotic behavior of the average-case filling volume for certain models of random Lipschitz cycles in the unit cube and sphere. For example, we estimate the minimal area of a Seifert surface for a model of random knots first studied by Millett. This is a generalization of the classical Ajtai--Koml\'os--Tusn\'ady optimal matching theorem from combinatorial probability. The author hopes for applications to the topology of random links, random maps between spheres, and other models of random geometric objects.

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Fedor Manin. 2020-08-25. Filling random cycles. https://doi.org/10.4171/cmh%2F520

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