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arXiv · 2009.06737

Lagrangian Skeleta and Plane Curve Singularities

Roger Casals
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Abstract

We construct closed arboreal Lagrangian skeleta associated to links of isolated plane curve singularities. This yields closed arboreal Lagrangian skeleta for Weinstein pairs and Weinstein 4-manifolds associated to max-tb Legendrian representatives of algebraic links. We provide computations of Legendrian and Weinstein invariants, and discuss the symplectic 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.

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Roger Casals. 2020-09-14. Lagrangian Skeleta and Plane Curve Singularities. https://arxiv.org/abs/2009.06737

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