Abstract
We study symplectic rigidity phenomena for fibers in cotangent bundles of Riemann surfaces. Our main result can be seen as a generalization to open Riemann surfaces of arbitrary genus of work of Eliashberg and Polterovich on the Nearby Lagrangian Conjecture for \(T^* \mathbb {R}^2\). As a corollary, we answer a strong version in dimension \(2n=4\) of a question of Eliashberg about linking of Lagrangian disks in \(T^* \mathbb {R}^n\), which was previously answered by Ekholm and Smith in dimensions \(2n \ge 8\).
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