Abstract:
In my talk I will conjecture existence of certain new homological invariants of closed 3-manifolds. The invariants provide a categorification of the analytically continued Witten-Reshetikhin-Turaev (WRT) invariant, have some similarities with Heegaard/monopole Floer homology and generalize Khovanov homology of knots to compact 3-manifolds. Physically such invariants can be defined as Hilbert spaces of M-theory in certain backgrounds. I will describe mathematical properties of such invariants, and how to calculate them for some specific types of 3-manifolds. The talk is mainly based on a joint work with S. Gukov, D. Pei and C. Vafa.