Topology Seminar

The Khovanov homology groups of the torus knots T(n,m) are known to stabilize as m goes to infinity with n fixed. In this talk, we make the observation that when n = 2, the stable limit happens to be isomorphic to the homology of the free loop space of the 2-sphere. Our main result suggests that this is not merely a coincidence: we prove that the k-colored sl(N) homology of T(2,m) stabilizes to the homology of the free loop space of the complex Grassmannian Gr(k,N).