Geodesic
Quantization of Whitney functions and reduction
Journal of Singularities, Tome 13 (2015), pp. 217-228

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For a possibly singular subset of a regular Poisson manifold we construct a deformation quantization of its algebra of Whitney functions. We then extend the construction of a deformation quantization to the case where the underlying set is a subset of a not necessarily regular Poisson manifold which can be written as the quotient of a regular Poisson manifold on which a compact Lie group acts freely by Poisson maps. Finally, if the quotient Poisson manifold is regular as well, we show a "quantization commutes with reduction" type result. For the proofs, we use methods stemming from both singularity theory and Poisson geometry. 
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     author = {M. J. Pflaum and H. Posthuma, and X. Tang},
     title = {Quantization of {Whitney} functions and reduction},
     journal = {Journal of Singularities},
     pages = {217--228},
     publisher = {mathdoc},
     volume = {13},
     year = {2015},
     doi = {10.5427/jsing.2015.13l},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2015.13l/}
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M. J. Pflaum; H. Posthuma,; X. Tang. Quantization of Whitney functions and reduction. Journal of Singularities, Tome 13 (2015), pp. 217-228. doi: 10.5427/jsing.2015.13l

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