Incorporating loop space coefficients into our Legendrian invariants

The Chekanov-Eliashberg differential graded algebra is an algebraic invariant associated to a Legendrian inside of a contact manifold. In a paper by Ekholm and Lekili, the authors propose an enriched version of this DGA which includes "loop space" coefficients. The authors present an interesting methods to incorporate loop space coefficients: use a family $f_{1},f_{2},\cdots$ of Morse functions to obtain a family of "push-offs" of the Legendrian, and to count disks with boundary on this family of "parallel" Legendrians. What does this have to do with loop space coefficeints? In this talk we will explore these ideas.

Zoom Seminar Link