The Gysin sequence and the sl(N) homology of T(2,m)

Abstract

The sl(N) homology of the torus knot or link T(2,m) may be calculated explicitly. By direct comparison, the result is isomorphic to the cohomology of a naturally associated space of SU(N) representations of the knot group. In honor of Tom Mrowka's 60th birthday, we explain how the Gysin exact sequence may be used to show that these groups are isomorphic without explicitly calculating them.