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.