An algebraic index theorem for orbifolds

Details An algebraic index theorem for orbifolds An algebraic index theorem for orbifolds

2005-07-26

arxiv.org/abs/math/0507546v2

Mathematics

K-Theory and Homology

34 pages, and presentation improved

Scientific paper

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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