Lagrangian fillings for Legendrian links of finite type

Abstract

We prove that there are at least seeds many exact embedded Lagrangian fillings for Legendrian links of type $\mathsf{ADE}$. We also provide seeds many Lagrangian fillings with certain symmetries for type $\mathsf{BCFG}$. Our main tools are $N$-graphs and the combinatorics of seed patterns of finite type.

46 pages