Open Gromov–Witten theory, skein modules, duality, and knot contact homology – T. Ekholm – ICM2018

Geometry | Topology
Invited Lecture 5.7 | 6.3
Open Gromov–Witten theory, skein modules, large N duality, and knot contact homology
Tobias Ekholm

Abstract: Large N duality relates open Gromov–Witten invariants in the cotangent bundle of the 3-sphere with closed Gromov–Witten invariants in the resolved conifold using physics arguments. It is a crucial result for the last twenty years of very successful interplay between Gromov–Witten theory and Chern–Simons gauge theory. We outline a symplectic geometric proof of large N duality which generalizes open Gromov–Witten invariants to invariants with values in the framed skein module and applies symplectic neck stretching. We then describe how knot contact homology and its generalizations capture the Gromov–Witten invariants ‘from infinity’ in comparatively simple terms.

ICM 2018 – International Congress of Mathematicians ©
 
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