The basic bundle gerbe on unitary groups, revisited
Danny Stevenson (University of Glasgow)
Monday 29th September, 2008 16:00-17:00 Mathematics Building, room 214
Let G be the unitary group U(n) or more generally one of the groups U_p(H) consisting of unitary operators on an infinite dimensional Hilbert space H which differ from the identity by an element of the Schatten ideal L^p. For these groups G, the degree three integer cohomology group H^3(G,Z) of G is canonically isomorphic to the integers Z. The generator of H^3(G,Z) = Z can be realized geometrically as the `basic bundle gerbe'. Building on work of Meinrenken and Mickelsson we will give a construction of this basic bundle gerbe. We will explain how the holomorphic functional calculus can be used to describe the geometry of this gerbe. This is joint work with Michael Murray.