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|Title:||Quantising proper actions on SpinC-manifolds|
|Citation:||Asian Journal of Mathematics, 2017; 21(4):631-686|
|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|
|Appears in Collections:||Mathematical Sciences publications|
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