Toric constructions of monotone Lagrangian submanifolds in $\mathbb{CP}^2$ and $\mathbb{CP}^1 \times \mathbb{CP}^1$

Miguel Abreu , Agnès Gadbled (1)

1 IF - Institut Fourier

We extract from a toric model of the Chekanov-Schlenk exotic torus in $\mathbb{CP}^2$ methods of construction of Lagrangian submanifolds in toric symplectic manifolds. These constructions allow for some control of the monotonicity. We recover this way some known monotone Lagrangians in the toric symplectic manifolds $\mathbb{CP}^2$ and $\mathbb{CP}^1 \times \mathbb{CP}^1$ as well as new examples.

Domaines: Mathématiques [math]

Miguel Abreu, Agnès Gadbled. Toric constructions of monotone Lagrangian submanifolds in $\mathbb{CP}^2$ and $\mathbb{CP}^1 \times \mathbb{CP}^1$. Journal of Symplectic Geometry, 2017, 15, ⟨10.4310/JSG.2017.v15.n1.a5⟩. ⟨hal-02404263⟩