Edward Witten: "From Gauge Theory to Khovanov Homology Via Floer Theory”

Institute for Pure & Applied Mathematics (IPAM)

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Green Family Lecture Series 2017
"From Gauge Theory to Khovanov Homology Via Floer Theory”
Edward Witten, Institute for Advanced Study
Abstract: The goal of the lecture is to describe a gauge theory approach to Khovanov homology of knots, in particular, to motivate the relevant gauge theory equations in a way that does not require too much physics background. I will give a gauge theory perspective on the construction of singly-graded Khovanov homology by Abouzaid and Smith.
Institute for Pure and Applied Mathematics, UCLA
March 6, 2017
For more information: www.ipam.ucla.e...

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1 окт 2024

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Комментарии : 7

@jospina65 Год назад

From Gauge Theory to Khovanov Homology via Spatial refinements: Starting from the equations KW and HW, certain framed flow category which I will name "Witten category" must be constructed. Using the Cohen-Jones-Segal mechanism acting on the Witten category, certain Witten spectrum is obtained. Then, the singular homology of the Witten spectrum is precisely the Khovanov homology.

@ConstructiveCriticHD 4 года назад

Skip to 4:08

@jospina65 5 лет назад

It is interesting to note that Professor Witten has outlined gauge theory interpretations of Khovanov homology and the Jones polynomial, in which the Seidel-Smith space (certain symplectic manifold) is viewed as the moduli space of solutions to the Bogomolny equations.