Date of Submission

Spring 2021

Academic Program

Mathematics

Project Advisor 1

Caitlin Leverson

Abstract/Artist's Statement

In the study of Legendrian knots, which are smoothly embedded circles constrained by a differential geometric condition, an actively-studied problem is to find conditions for the existence of Lagrangian cobordisms, which are Lagrangian surfaces whose slices specific Legendrian knots at either end. Any topological knot has infinitely many distinct Legendrian representatives, which are partially distinguished by the Thurston-Bennequin number tb, an integer invariant of Legendrian isotopy which is bounded above. We demonstrate a family of knots where each has a maximal-tb representative K admitting a Lagrangian cobordism from a stabilized Legendrian unknot, a property which guarantees the existence of a similar cobordism from stabilized unknots to any representatives resulting from stabilization of K.

Open Access Agreement

Open Access

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License.

Additional Files
Dubrovnik Pretzel Mathematica.nb (44 kB)
Mathematica Notebook containing code for computation of $\maxtb P(3, -3, n)$.
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