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arXiv · 2004.04233

Symplectic Rigidity of Fibers in Cotangent Bundles of Open Riemann Surfaces

Laurent Côté·Georgios Dimitroglou Rizell
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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 $2n \geq 8$.

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Laurent Côté, Georgios Dimitroglou Rizell. 2020-04-08. Symplectic Rigidity of Fibers in Cotangent Bundles of Open Riemann Surfaces. https://arxiv.org/abs/2004.04233

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