Lagrangian skeleta and plane curve singularities

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 ) . W...

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Bibliographic Details
Published in:Journal of fixed point theory and applications Vol. 24; no. 2
Main Author: Casals, Roger
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.06.2022
Subjects:
Analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Symplectic geometry - A Festschrift in honour of Claude Viterbo’s 60th birthday
53D12
14H20
57K33
ISSN:1661-7738, 1661-7746
Online Access:Get full text
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Summary: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.
ISSN:1661-7738
1661-7746
DOI:10.1007/s11784-022-00939-8