Lagrangian fillings for Legendrian links of affine type
Abstract
We prove that there are at least as many exact embedded Lagrangian fillings as seeds for Legendrian links of affine type $\tilde{\mathsf{D}} \tilde{\mathsf{E}}$. We also provide as many Lagrangian fillings with certain symmetries as seeds of type $\tilde{\mathsf{B}}_n$, $\tilde{\mathsf{F}}_4$, $\tilde{\mathsf{G}}_2$, and $\mathsf{E}_6^{(2)}$. These families are the first known Legendrian links with infinitely many fillings that exhaust all seeds in the corresponding cluster structures. Furthermore, we show that Legendrian realization of Coxeter mutation of type $\tilde{\mathsf{D}}$ corresponds to the Legendrian loop considered by Casals and Ng.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.04283
 Bibcode:
 2021arXiv210704283A
 Keywords:

 Mathematics  Symplectic Geometry;
 Mathematics  Combinatorics;
 Mathematics  Geometric Topology;
 Primary: 53D10;
 13F60. Secondary: 57R17
 EPrint:
 46pages