Bordered Legendrian Rational Symplectic Field Theory

Abstract

Given a Legendrian knot $\Lambda \subset \mathbb{R}^3$ and a vertical line dividing the front projection of $\Lambda$ into two halves, we construct a differential graded algebra associated to each half-knot. We then show that one may obtain the commutative algebra from Legendrian Rational Symplectic Field Theory as a pushout of the two bordered algebras. This construction extends the bordered Chekanov-Eliashberg differential graded algebra by incorporating disks with multiple positive punctures into the differential.