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Two Lectures on the Jones Polynomial and Khovanov Homology
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In the first of these two lectures I describe a gauge theory approach to understanding quantum knot invariants as Laurent polynomials in a complex variable q. The two main steps are to reinterpret three-dimensional Chern-Simons gauge theory in four dimensional terms and then to apply electric-magnetic duality. The variable q is associated to instanton number in the dual description in four dimensions. In the second lecture, I describe how Khovanov homology can emerge upon adding a fifth dimension.
Title: Two Lectures on the Jones Polynomial and Khovanov Homology
Description:
In the first of these two lectures I describe a gauge theory approach to understanding quantum knot invariants as Laurent polynomials in a complex variable q.
The two main steps are to reinterpret three-dimensional Chern-Simons gauge theory in four dimensional terms and then to apply electric-magnetic duality.
The variable q is associated to instanton number in the dual description in four dimensions.
In the second lecture, I describe how Khovanov homology can emerge upon adding a fifth dimension.
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