Surface Operators and Knot Homologies

  • Sergei GukovEmail author
Conference paper


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.


Gauge Theory Modulus Space Topological String Surface Operator Braid Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of CaliforniaSanta BarbaraUSA

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