The authors construct cluster structures on sheaf moduli of twist-spun Legendrian surfaces and use them to produce new exact Lagrangian fillings and obstructions in contact R^5.
Lagrangian fillings for Legendrian links of finite type
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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.
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Legendrian doubles, twist spuns, and clusters
The authors construct cluster structures on sheaf moduli of twist-spun Legendrian surfaces and use them to produce new exact Lagrangian fillings and obstructions in contact R^5.