Block, Jonathan; Getzler, Ezra Quantization of foliations. (English) Zbl 0812.58028 Catto, Sultan (ed.) et al., Differential geometric methods in theoretical physics. Proceedings of the 20th international conference, June 3-7, 1991, New York City, NY, USA. Vol. 1-2. Singapore: World Scientific. 471-487 (1992). Summary: Using Gerstenhaber’s deformation theory, we develop an analogue of the Poisson bracket for foliations associated to pre-symplectic manifolds. Our motivation for this is to understand better the algebra of Fourier integral operators associated to a coisotropic submanifold of the cotangent bundle by Guillemin, Sternberg and Uribe.For the entire collection see [Zbl 0801.00032]. Cited in 1 ReviewCited in 14 Documents MSC: 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\) 46L85 Noncommutative topology 46L87 Noncommutative differential geometry 53D50 Geometric quantization 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) Keywords:non-commutative geometry; deformation; Poisson bracket; foliations; pre- symplectic manifolds PDFBibTeX XMLCite \textit{J. Block} and \textit{E. Getzler}, in: Differential geometric methods in theoretical physics. Proceedings of th 20th international conference, June 3-7, 1991, New York City, NY, USA. Vol. 1-2. Singapore: World Scientific. 471--487 (1992; Zbl 0812.58028)