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}
}
  • P. Hochs, V. Mathai
  • Published 2017
  • Mathematics
  • Asian Journal of Mathematics
  • 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
    17 Citations

    References

    SHOWING 1-10 OF 37 REFERENCES
    Quantisation of presymplectic manifolds, K-theory and group representations
    • 15
    • PDF
    Quantisation commutes with reduction at discrete series representations of semisimple groups
    • 25
    • PDF
    The Guillemin-Sternberg conjecture for noncompact groups and spaces
    • 26
    • PDF
    The index theory on non-compact manifolds with proper group action
    • 20
    • Highly Influential
    • PDF
    Localization of the Riemann–Roch Character
    • 92
    • PDF
    Symplectic Surgery and the Spinc–Dirac Operator
    • 161
    • PDF
    Geometric quantization and families of inner products
    • 28
    • PDF
    Functorial quantization and the Guillemin-Sternberg conjecture ∗
    • 9