Surface Operators and Knot Homologies

Understand

Topological gauge theories in four dimensions which admit surface operators provide a natural framework for realizing homological knot invariants.

• Every such theory leads to an action of the braid group on branes on the corresponding moduli space.
• This action plays a key role in the construction of homological knot invariants.
• We illustrate the general construction with examples based on surface operators in N=2 and N=4 twisted gauge theories which lead to a categorification of the Alexander polynomial, the equivariant knot signature, and certain analogs of the Casson invariant.