Lagrangian Skeleta and Plane Curve Singularities
Symplectic Geometry
2020-09-16 v1 Algebraic Geometry
Geometric Topology
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.
Cite
@article{arxiv.2009.06737,
title = {Lagrangian Skeleta and Plane Curve Singularities},
author = {Roger Casals},
journal= {arXiv preprint arXiv:2009.06737},
year = {2020}
}
Comments
27 Pages, 11 Figures