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An algebraic index theorem for orbifolds

Markus J. Pflaum·Hessel Posthuma·Xiang Tang
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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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BibTeXRIS

Markus J. Pflaum, Hessel Posthuma, Xiang Tang. 2005-09-13. An algebraic index theorem for orbifolds. https://arxiv.org/abs/math/0507546

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