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arXiv · 1408.0085

Quantising proper actions on Spin$^c$-manifolds

Peter Hochs·Varghese Mathai
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Abstract

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-cocompact case, the result generalises to Spin$^c$-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.

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BibTeXRIS

Peter Hochs, Varghese Mathai. 2014-08-01. Quantising proper actions on Spin$^c$-manifolds. https://doi.org/10.4310/ajm.2017.v21.n4.a2

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