Free loop spaces and link homology
Free loop spaces and link homology

Joshua Wang, Princeton/IAS
Fine Hall 314
The Khovanov homology groups of 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 2sphere. Our main result suggests that this is not merely a coincidence: we prove that the kcolored sl(N) homology of T(2,m) stabilizes to the homology of the free loop space of the complex Grassmannian Gr(k,N). We also relate the space of closed geodesics on the Grassmannian to the kcolored sl(N) homologies of the individual torus knots T(2,m).