Twisted K-homology and group-valued moment maps

Details Twisted K-homology and group-valued moment maps Twisted K-homology and group-valued moment maps

2010-08-06

arxiv.org/abs/1008.1261v1

Mathematics

Differential Geometry

38 pages

Scientific paper

Let G be a compact, simply connected Lie group. We develop a `quantization functor' from pre-quantized quasi-Hamiltonian G-spaces at level k to the fusion ring (Verlinde algebra) R_k(G). The quantization Q(M) is defined as a push-forward in twisted equivariant K-homology. It may be computed by a fixed point formula, similar to the equivariant index theorem for Spin_c-Dirac operators. Using the formula, we calculate Q(M) in several examples.

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