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arXiv · 2608.10493

On orderability and the chord conjecture

Egor Shelukhin
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Abstract

We prove Arnol'd's chord conjecture for a large new class of contact manifolds: for every contact form and every closed Legendrian submanifold there exists a non-constant Reeb chord with endpoints on the Legendrian. This class is characterized by contact non-orderability and rigidity of symplectizations. This proves the chord conjecture for Brieskorn manifolds, many prequantization spaces, and for all prequantization spaces under a mild topological condition on the Legendrians. Moreover, it provides a uniform upper bound on the length of the minimal chord. Our approach involves a new link between Mohnke's construction and contact Hofer geometry.

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Egor Shelukhin. 2026-08-11. On orderability and the chord conjecture. https://arxiv.org/abs/2608.10493

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