# Two Lectures On The Jones Polynomial And Khovanov Homology

@inproceedings{Witten2014TwoLO, title={Two Lectures On The Jones Polynomial And Khovanov Homology}, author={Edward Witten}, year={2014} }

- Published 2014

In the rst 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

#### Citations

##### Publications citing this paper.

SHOWING 1-10 OF 14 CITATIONS

## A sheaf-theoretic model for SL(2,C) Floer homology

VIEW 2 EXCERPTS

CITES METHODS

## Root systems, spectral curves, and analysis of a Chern-Simons matrix model for Seifert fibered spaces

VIEW 1 EXCERPT

CITES BACKGROUND

## The Extended Bogomolny Equations and Generalized Nahm Pole Boundary Condition

VIEW 1 EXCERPT

CITES BACKGROUND

## Two Lectures on Gauge Theory and Khovanov Homology

VIEW 1 EXCERPT

CITES BACKGROUND

## Algebra of the Infrared: String Field Theoretic Structures in Massive ${\cal N}=(2,2)$ Field Theory In Two Dimensions

VIEW 2 EXCERPTS

CITES BACKGROUND

## An Introduction To The Web-Based Formalism

VIEW 1 EXCERPT

CITES BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 45 REFERENCES

## Fivebranes And Knots

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## Branes and Supergroups

VIEW 1 EXCERPT

## Fukaya-Seidel category and gauge theory

VIEW 1 EXCERPT

## Odd Khovanov homology

VIEW 1 EXCERPT

## The Nahm Pole Boundary Condition

VIEW 2 EXCERPTS

## Geometric aspects of the Kapustin–Witten equations

VIEW 1 EXCERPT

## Khovanov Homology and Gauge Theory

VIEW 2 EXCERPTS

## Knot invariants from four-dimensional gauge theory

VIEW 1 EXCERPT