Rigidity of multisections to the universal cubic plane curve

arXiv Math

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Abstract

We study the following question of Farb: For which positive integers n is it possible to choose n distinct points continuously on every smooth cubic plane curve?

This paper is a continuation of the work of Banerjee-Chen.

We prove that such choice is unique up to homotopy for n=27 (smallest open case), and does not exist for n=36k+18.

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Rigidity of multisections to the universal cubic plane curve

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