Deformation Quantization of Surjective Submersions

In this talk I will discuss a definition of what a deformation quantization of a surjective submersion should be. Using a purely cohomological approach yields existence and classification up to a natural notion of equivalence. The main application is the deformation quantization of principal fiber bundles which I will discuss in some detail. In particular, they can still be used to associate vector bundles, now in the deformed framework.