Journal of Singularities
volume 13 (2015), 217-228
Received 23 October 2013.
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.
|Markus J. Pflaum||Hessel Posthuma||Xiang Tang|
|Department of Mathematics||Korteweg-de Vries Institute for Mathematics||Department of Mathematics|
|University of Colorado||University of Amsterdam||Washington University|
|Boulder, USA||The Netherlands||St. Louis, USA|
|email: email@example.com||email: firstname.lastname@example.org||email: email@example.com|