Augmentations and ruling polynomials for Legendrian graphs

Abstract: In this talk, we will show the equivalence between two Legendrian isotopy invariants of Legendrian graphs: (i) augmentation number via point-counting over a finite field for the augmentation variety of the associated Chekanov-Eliashberg DGA, and (ii) the ruling polynomial via combinatorics of the decompositions of the associated front projections. This is a joint work with Youngjin Bae(Incheon National University) and Tao Su(Yau Mathematical Sciences Center, Tsinghua University).

algebraic geometryalgebraic topologycomplex variablesdifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

2021 Pacific Rim Complex & Symplectic Geometry Conference