Geometric quantization for proper actions

Details Geometric quantization for proper actions Geometric quantization for proper actions

2008-06-19

arxiv.org/abs/0806.3138v3

Advances in Mathematics225:1224-1247, 2010

Mathematics

Differential Geometry

20 pages. Appendix by Ulrich Bunke. To appear in, Advances in Mathematics

Scientific paper

10.1016/j.aim.2010.03.023

We first introduce an invariant index for G-equivariant elliptic differential operators on a locally compact manifold M admitting a proper cocompact action of a locally compact group G. It generalizes the Kawasaki index for orbifolds to the case of proper cocompact actions. Our invariant index is used to show that an analog of the Guillemin-Sternberg geometric quantization conjecture holds if M is symplectic with a Hamiltonian action of G that is proper and cocompact. This essentially solves a conjecture of Hochs and Landsman.

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