Abstract:

In this talk I would discuss about an approach to Jones polynomial and Khovanov homolgy via gauge theory introduced by E. Witten. Starting from the system of D3-NS5 branes, which can be related to a Chern-Simons gauge theory on the boundary of the D3-brane, with the standard techniques of S and T duality, we can calculate manifestly invariant description of Jones polynomial and Khovanov homology using Kapustin-Witten equations.