An algebraic index theorem for orbifolds
K-Theory and Homology
2007-05-23 v2 Mathematical Physics
math.MP
Symplectic Geometry
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.
Cite
@article{arxiv.math/0507546,
title = {An algebraic index theorem for orbifolds},
author = {Markus J. Pflaum and Hessel Posthuma and Xiang Tang},
journal= {arXiv preprint arXiv:math/0507546},
year = {2007}
}
Comments
34 pages, and presentation improved