Abstract
For a possibly singular subset of a regular Poisson manifold we construct a deformation of its algebra of Whitney functions. We then extend the construction of a deformation 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have