GROUP COCYCLES ON LOOP GROUPS

In this talk, we start out by reviewing the construction of central extensions of smooth loop groups and their relationship to the tame symbol of a pair of meromorphic functions on a Riemann surface. Our goal is then to introduce higher central extensions of smooth double loop groups. In this process, we shall see how to combine operator theoretic techniques relating to perturbations of Fredholm operators on Hilbert spaces with concepts from higher category theory. The talk is based on joint work with Ryszard Nest and Jesse Wolfson.