Twisted K-Homology and Group-Valued Moment Maps

By E. Meinrenken. 2010

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Let G be a compact, simply connected Lie group. We develop a ‘quantization functor’ from prequantized quasi-Hamiltonian G-spaces (M,ω,Φ) at level k to the fusion ring (Verlinde algebra) R k (G). The quantization 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 in several examples.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/74f5048821e6db94d1edc91016c3980d1612a0b0