Georgia Institute of Technology College of Sciences

In high dimensional contact and symplectic topology, finding interesting constructions for Legendrian submanifolds is an active area of research. Further, it is desirable that the constructions lend themselves nicely to computation of invariants. The doubling construction was defined by Ekholm, which uses Lagrangian fillings of a Legendrian knot in standard contact R^{2n-1} to produce a closed Legendrian submanifold in standard contact R^{2n+1}. Later Courte-Ekholm showed that symmetric doubles of embedded fillings are "uninteresting". In recent work the symmetric doubling construction was generalised to any contact manifold, giving two isotopic constructions related to open book decompositions of the ambient manifold. In a separate joint work with James Hughes, we explore the asymmetric doubling construction through Legendrian weaves.