Journal of Symplectic Geometry

Volume 15 (2017)

Number 1

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

Pages: 151 – 187



Miguel Abreu (Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, Universidade de Lisboa, Portugal)

Agnès Gadbled (Departamento de Matemática da FCUP, Universidade do Porto, Portugal)


We extract from a toric model of the Chekanov–Schlenk exotic torus in $\mathbb{CP}^2$ methods for constructing Lagrangian submanifolds in toric symplectic manifolds. These constructions allow for some control of 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.

Published 28 April 2017