Quantising proper actions on $\mathrm{Spin}^c$-manifolds
@article{Hochs2017QuantisingPA,
title={Quantising proper actions on \$\mathrm\{Spin\}^c\$-manifolds},
author={P. Hochs and V. Mathai},
journal={Asian Journal of Mathematics},
year={2017},
volume={21},
pages={631-686}
}Paradan and Vergne generalised the quantisation commutes with reduction principle of Guillemin and Sternberg from symplectic to Spin$^c$-manifolds. We extend their result to noncompact groups and manifolds. This leads to a result for cocompact actions, and a result for non-cocompact actions for reduction at zero. The result for cocompact actions is stated in terms of $K$-theory of group $C^*$-algebras, and the result for non-cocompact actions is an equality of numerical indices. In the non… CONTINUE READING
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