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. This paper is based on a lecture delivered at the International Congress on Mathematical Physics 2006, Rio de Janeiro, and at the RTN Workshop 2006, Napoli.
CITATION STYLE
Gukov, S. (2009). Surface Operators and Knot Homologies. In New Trends in Mathematical Physics (pp. 313–343). Springer Netherlands. https://doi.org/10.1007/978-90-481-2810-5_22
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