Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Shelukhin, Egor
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7202275775
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