Legendrian knots, Lagrangian fillings, and Cluster algebras

Abstract: Classifications of Legendrian knots and their exact Lagrangian fillings are central questions in low-dimensional contact and symplectic topology. Recent development suggests that one can distinguish exact Lagrangian fillings by applying tools from cluster algebras. In this talk, we focus on Legendrian links that are obtained as the rainbow closure of positive braids. We prove that any positive braid Legendrian link not isotopic to a standard finite type link admits infinitely many exact Lagrangian fillings. The main techniques of its proof include cluster algebras and Chekanov-Eliashberg differential graded algebras. This is joint work with Honghao Gao and Daping Weng.

Mathematics

Audience: researchers in the topic

ICCM 2020