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Journal of Homotopy and Related Structures

, Volume 11, Issue 3, pp 409–424 | Cite as

Formal geometric quantisation for proper actions

  • Peter Hochs
  • Varghese Mathai
Article

Abstract

We define formal geometric quantisation for proper Hamiltonian actions by possibly noncompact groups on possibly noncompact, prequantised symplectic manifolds, generalising work of Weitsman and Paradan. We study the functorial properties of this version of formal geometric quantisation, and relate it to a recent result by the authors via a version of the shifting trick. For (pre)symplectic manifolds of a certain form, quantisation commutes with reduction, in the sense that formal quantisation equals a more direct version of quantisation.

Keywords

Geometric quantisation Group \(C^*\)-algebras \(K\)-homology 

Notes

Acknowledgments

The authors would like to thank Paul-Émile Paradan for helpful comments.

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Copyright information

© Tbilisi Centre for Mathematical Sciences 2015

Authors and Affiliations

  1. 1.School of Mathematical SciencesThe University of AdelaideAdelaideAustralia

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