Lagrangian cobordisms, enriched knot diagrams, and algebraic invariants
We introduce new invariants to the existence of Lagrangian
cobordisms in R^4. These are obtained by studying holomorphic disks
with corners on Lagrangian tangles, which are Lagrangian cobordisms
with flat, immersed boundaries.
We develop appropriate sign conventions and results to characterize
boundary points of 1-dimensional moduli spaces with boundaries on
Lagrangian tangles. We then use these to define (SFT-like) algebraic
structures that recover the previously described obstructions.
This talk is based on my thesis work under the supervision of Y.
Eliashberg and on work in progress joint with J. Sabloff.
Member, School of Mathematics