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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].

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.)
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