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

Symplectic geometry and topology

17 November 14:00 - 15:00

Agnès Gadbled - Centro de Matemática da Universidade do Porto

In a previous paper, I proved that two very different constructions of monotone Lagrangian tori are Hamiltonian isotopic inside $\mathbb{CP}^2$ by comparing both of them to a third one called modified Chekanov torus. This modified Chekanov torus has an interesting projection under the standard moment map of $\mathbb{CP}^2$ and motivates a method of construction of (monotone) Lagrangian submanifolds in symplectic toric manifolds. I will explain how this method gives some old and new monotone examples in $\mathbb{CP}^2$ and $\mathbb{CP}^1 \times \mathbb{CP}^1$.
Tobias Ekholm,
Uppsala University
Yakov Eliashberg
Stanford University
Lenhard Ng
Duke University
Ivan Smith
University of Cambridge


Tobias Ekholm


For practical matters at the Institute, send an e-mail to