Licentiate Seminar: Extension Of The Chekanov–Eliashberg Algebra Using Annuli

Abstract: We define an SFT-type invariant for Legendrian knots in the standard contact R3. The invariant is a deformation of the Chekanov–Eliashberg differential graded algebra. The differential consists of a part that counts index zero J-holomorphic disks with up to two positive punctures, annuli with one positive puncture, and a string topological part. We describe the invariant and demonstrate its invariance combinatorially from the Lagrangian knot projection, and compute some simple examples where the deformation is non-vanishing.

Superviser is Tobias Ekholm and external examinar is Russell Avdek from Sorbonne Université