2017/11/16 by Ekholm, Tobias
#53D37 #53D42 (Primary) #53D45 #57M25 (Secondary) #57R25 #FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.1711.06316
Knot contact homology studies symplectic and contact geometric properties of conormals of knots in 3-manifolds using holomorphic curve techniques. It has connections to both mathematical and physical theories. On the mathematical side, we review the theory, show that it gives a complete knot invariant, and discuss its connections to Fukaya categories, string topology, and micro-local sheaves. On the physical side, we describe the connection between the augmentation variety of knot contact homology and Gromov-Witten disk potentials, and discuss the corresponding higher genus relation that quantizes the augmentation variety.