Examples/classes:
Types
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).
See also:
An algorithm for computing the Jones polynomial on a topological quantum computer based on anyon statistics:
The identification of the Jones polynomial with Wilson loop observables in Chern-Simons theory is due to
see also
Volume 126, Number 1 (1989), 167-199 (euclid.cmp/1104179728)
Lecture notes:
The categorification of this relation to an identification of Khovanov homology with observables in D=4 super Yang-Mills theory:
Edward Witten, Khovanov homology and gauge theory, arxiv/1108.3103
Edward Witten, Fivebranes and Knots (arXiv:1101.3216)
Lecture notes:
See also
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