# Distinguishing Clifford and Chekanov Lagrangian tori in $\C^2$ and $\CP^2$ via count of J-holomorphic discs.

• Renato Vianna (Cambridge)
• Friday 14 November 2014, 15:00-16:00
• MR13.

In 1995, Chekanov came up with the first example of monotone Lagrangian torus not Hamiltonian isotopic to the product torus $\times_n S1 \subset \Cn$, also called Clifford torus. Both tori also has its manifestation in $\CPn$ (and other compactifications of $\Cn$).

One technique to distinguish between monotone Lagrangian tori is via the count of (Maslov index 2) J-holomorphic discs. We will define the Clifford and Chekanov tori in $\C2$ and $\CP2$, and count the (Maslov index 2) holomorphic discs they bound.

We will not assume any knowledge of symplectic geometry and provide all necessary definitions in the talk.

This talk is part of the Junior Geometry Seminar series.