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. 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 a symplectic manifold with a singularity that becomes removable when described in terms 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. I will construct this algebra explicitly and interpret it as noncommutative geometry generated by the singularity.

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