Augmentations, Annuli, and Alexander polynomials

Date: 2020-09-03

Time: 14:00 - 15:00

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Luís Diogo

I will explain a formula for the Alexander polynomial of a knot in terms of the augmentation polynomial of the knot. The latter is obtained from knot contact homology, which is an invariant of the knot defined via counts of pseudoholomorphic curves. The proof involves studying pseudoholomorphic annuli and strips in the cotangent bundle of Euclidean 3-space, with Lagrangian boundary conditions. This is joint work with Tobias Ekholm.