Uniqueness of Lagrangians in $T^*RP2$

Nikolaos Adaloglou

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arXiv · 2201.09299

Uniqueness of Lagrangians in $T^*RP2$

Nikolaos Adaloglou

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Abstract

We present a new and simpler proof of the fact that any Lagrangian $\mathbb{R}P^2$ in $T^*\mathbb{R}P^2$ is Hamiltonian isotopic to the zero section. Our proof mirrors the one given by Li and Wu for the Hamiltonian uniqueness of Lagrangians in $T^*S^2$, using surgery to turn Lagrangian spheres into symplectic ones. The main novel contribution is a detailed proof of the folklore fact that the complement of a symplectic quadric in $\mathbb{C}P^2$ can be identified with the unit cotangent disc bundle of $\mathbb{R}P^2$.

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BibTeX RIS

Nikolaos Adaloglou. 2022-01-23. Uniqueness of Lagrangians in $T^*RP2$. https://arxiv.org/abs/2201.09299

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