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Type: Journal article
Title: Quantising proper actions on SpinC-manifolds
Author: Hochs, P.
Mathai, V.
Citation: The Asian Journal of Mathematics, 2017; 21(4):631-686
Publisher: International Press
Issue Date: 2017
ISSN: 1093-6106
Statement of
Peter Hochs and Varghese Mathai
Abstract: Paradan and Vergne generalised the quantisation commutes with reduction principle of Guillemin and Sternberg from symplectic to SpinC-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-cocompact case, the result generalises to SpinC-Dirac operators twisted by vector bundles. This yields an index formula for Braverman's analytic index of such operators, in terms of characteristic classes on reduced spaces.
Keywords: Geometric quantisation; quantisation commutes with reduction; proper Lie group actions; concompact index theorem
Rights: Copyright status unknown
DOI: 10.4310/AJM.2017.v21.n4.a2
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