Gauge theory and knot homologies

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 a simple example based on surface operators in N = 4 twisted gauge theory which cad to a categori ti cation of a variant of the Casson invariant. (C) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.