The noncommutative geometry of a singular symplectic manifold
Christian Blohmann (MPI Bonn)
Wednesday 23rd November, 2011 16:00-17:00 204
Traditionally, prequantization constructs a representation of the Lie algebra of functions on a symplectic manifold by operators on the space of sections of a line bundle.Â First, I will explain how this can be generalized by associating a Lie algebroid to the symplectic manifold, integrating it to a Lie groupoid, and constructing the groupoid convolution algebra. Then I give an example of aÂ symplectic manifold with a singularity that becomes removable when described in termsÂ of the Lie algebroid. As a consequence, its prequantization via groupoids leads to an algebra that is different from the one obtained by the traditional method.Â I will construct this algebra explicitly and interpret it as noncommutative geometry generated by the singularity.