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On the deformation quantization of symplectic orbispaces

Markus J. Pflaum
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Abstract

In the first part of this article we provide a geometrically oriented approach to the theory of orbispaces which originally had been introduced by Chen. We explain the notion of a vector orbibundle and characterize the good sections of a reduced vector orbibundle as the smooth stratified sections. In the second part of the article we elaborate on the quantizability of a symplectic orbispace. By adapting Fedosov's method to the orbispace setting we show that every symplectic orbispace has a deformation quantization. As a byproduct we obtain that every symplectic orbifold possesses a star product.

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Markus J. Pflaum. 2002-08-14. On the deformation quantization of symplectic orbispaces. https://arxiv.org/abs/math-ph/0208020

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