1. Characteristic classes of star products on Marsden-Weinstein reduced symplectic manifolds
- Author
-
Thorsten Reichert
- Subjects
Pure mathematics ,FOS: Physical sciences ,01 natural sciences ,Star product ,0103 physical sciences ,Mathematics - Quantum Algebra ,FOS: Mathematics ,Equivariant cohomology ,Quantum Algebra (math.QA) ,Astrophysics::Solar and Stellar Astrophysics ,0101 mathematics ,Mathematics::Symplectic Geometry ,Astrophysics::Galaxy Astrophysics ,Mathematical Physics ,Mathematics ,010308 nuclear & particles physics ,010102 general mathematics ,Kirwan map ,Statistical and Nonlinear Physics ,Mathematical Physics (math-ph) ,53D55 ,Manifold ,Cohomology ,Characteristic class ,Mathematics - Symplectic Geometry ,Cartan model ,Symplectic Geometry (math.SG) ,Astrophysics::Earth and Planetary Astrophysics ,Symplectic geometry - Abstract
In this note we consider a quantum reduction scheme in deformation quantization on symplectic manifolds proposed by Bordemann, Herbig and Waldmann based on BRST cohomology. We explicitly construct the induced map on equivalence classes of star products which will turn out to be an analogue to the Kirwan map but in the Cartan model of equivariant cohomology. As a byproduct we shall see that every star product on a (suitable) reduced manifold is equivalent to a reduced star product., updated to published version
- Published
- 2016