2007
DOI: 10.1016/j.aim.2006.05.018
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An algebraic index theorem for orbifolds

Abstract: Using the concept of a twisted trace density on a cyclic groupoid, a trace is constructed on a formal deformation quantization of a symplectic orbifold. An algebraic index theorem for orbifolds follows as a consequence of a local Riemann-Roch theorem for such densities. In the case of a reduced orbifold, this proves a conjecture by Fedosov, Schulze, and Tarkhanov. Finally, it is shown how the Kawasaki index theorem for elliptic operators on orbifolds follows from this algebraic index theorem.

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Cited by 22 publications
(37 citation statements)
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“…(We have used the notation C ∞,+ G for the groupoid convolution algebra with a unit adjoined.) We refer to [17,Sec. 1] for the details of this construction.…”
Section: An Index Theorem For Orbifoldsmentioning
confidence: 99%
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“…(We have used the notation C ∞,+ G for the groupoid convolution algebra with a unit adjoined.) We refer to [17,Sec. 1] for the details of this construction.…”
Section: An Index Theorem For Orbifoldsmentioning
confidence: 99%
“…We need to develop some Lie algebra cohomology tools as in [17,Sec. 5] in order to obtain a full answer to the above question.…”
Section: Algebraic Index Pairingmentioning
confidence: 99%
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