Lagrangian skeleta and plane curve singularities - Casals, Roger (Journal of fixed point theory and applications, 2022)
We construct closed arboreal Lagrangian skeleta associated to links of isolated plane curve singularities. This yields closed Lagrangian skeleta for Weinstein pairs ( C 2 , Λ ) and Weinstein 4-manifolds W ( Λ ) associated to max-tb Legendrian representatives of algebraic links Λ ⊆ ( S 3 , ξ st ) . We provide computations of Legendrian and Weinstein invariants, and discuss the contact topological nature of the Fomin–Pylyavskyy–Shustin–Thurston cluster algebra associated to a singularity. Finally, we present a conjectural ADE-classification for Lagrangian fillings of certain Legendrian links and list some related problems.