A great deal of work has been done in recent years to construct algebraic invariants ofLegendrian knots, and their higher-dimensional analogues. Here we employ the diagram- matic calculus developed in [3], in order to develop an iterative method for computing the so-called vexillary functions of a class of Legendrian surfaces. These give explicit point counts (over finite fields) of the moduli space of microlocal rank 1 sheaves, microsupported on a given surface. Our methods are largely inspired by a similar algorithm in the context of Legendrian braid closures, developed in [16]. Using our computations, we are also able to prove the nonexistence of Lagrangian fillings for the Legendrians in question.

Creator

• Snadden, John Arthur

DOI

• https://doi.org/10.21985/n2-bhh7-pf07

Subject

• Mathematics

Language

• en

Alternate Identifier

• http://dissertations.umi.com/northwestern:16484
• etdadmin_upload_980155

Keyword

• Moduli
• Legendrian
• Knot
• Combinatorics
• Microlocal

Date created

• 2023-01-01

Resource type

• Dissertation

Rights statement

• In Copyright