Link Invariants
Examples
Related concepts
The Jones polynomial is a knot invariant. It is a special case of the HOMFLY-PT polynomial. See there for more details.
In (Witten 89) it was shown that the Jones polynomial as a polynomial in $q$ is equivalently the partition function of $SU(2)$-Chern-Simons theory with a Wilson loop specified by the given knot as a function of the exponentiated level of the Chern-Simons theory. Extensive lecture notes on this are in (Witten 13a).
Later in (Witten 11) this identification was further refined to a correspondence between Khovanov homology and observables in 4-dimensional super Yang-Mills theory. Extensive lectures notes on this are in (Witten 13b).
The identification of the Jones polynomial with the partition function of Chern-Simons theory with Wilson loops is due to
The further identification of this with via the Khovanov homology induced by a 4-dimensional super Yang-Mills theory is due to
Edward Witten, Khovanov homology and gauge theory, arxiv/1108.3103
Edward Witten, Fivebranes and Knots (arXiv:1101.3216)
Lecture notes on this are in
Edward Witten, A New Look At The Jones Polynomial of a Knot, Clay Conference, Oxford, October 1, 2013 (pdf)
Edward Witten, Khovanov Homology And Gauge Theory, Clay Conference, Oxford, October 2, 2013 (pdf)
See also
Last revised on October 4, 2013 at 12:42:47. See the history of this page for a list of all contributions to it.