A Diagrammatic Calculus for Legendrian Surfaces

Abstract: I will describe work with Roger Casals. We show how planar diagrams called N-graphs encode Legendrian surfaces which cover the plane N-to-1. These N-graphs can be used to express Reidemeister moves, surgeries, and connect sums; to describe a Markov move a` la braids; to construct large classes of examples of any genus; to define moduli spaces which can be used to distinguish surfaces up to Legendrian isotopy; to discuss cluster charts and mutations; to construct exact Lagrangian fillings; and to define a planar algebra.

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar