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Title: Cubic Planar Graphs and Legendrian Surface Theory
We study Legendrian surfaces determined by cubic planar graphs. Graphs with distinct chromatic polynomials determine surfaces that are not Legendrian isotopic, thus giving many examples of non-isotopic Legendrian surfaces with the same classical invariants. The Legendrians have no exact Lagrangian fillings, but have many interesting non-exact fillings. We obtain these results by studying sheaves on a three-ball with microsupport in the surface. The moduli of such sheaves has a concrete description in terms of the graph and a beautiful embedding as a holomorphic Lagrangian submanifold of a symplectic period domain, a Lagrangian that has appeared in the work of Dimofte–Gabella–Goncharov. We exploit this structure to find conjectural open Gromov–Witten invariants for the non-exact filling, following Aganagic–Vafa.  more » « less
Award ID(s):
1708503
PAR ID:
10104517
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Advances in theoretical and mathematical physics
Volume:
22
Issue:
5
ISSN:
1095-0761
Page Range / eLocation ID:
1289-1345
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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