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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.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's version

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Publisher copy:
10.1016/j.aim.2006.05.018

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Institution:
Goethe-Universität Frankfurt/Main
Department:
Fachbereich Mathematik
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Institution:
University of Oxford
Department:
Mathematical,Physical & Life Sciences Division - Mathematical Institute
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Institution:
University of California, Davis
Department:
Department of Mathematics
Publisher:
Elsevier Inc. Publisher's website
Journal:
Advances in Mathematics Journal website
Volume:
210
Issue:
1
Pages:
83–121
Publication date:
2007-03-05
DOI:
ISSN:
0001-8708
URN:
uuid:c26af0d5-60a9-4dde-9eec-a5b62e41dc91
Local pid:
ora:8078

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