Poisson geometry and deformation quantization near a strictly pseudoconvex boundary

DOI10.4171/JEMS/93zbMath1146.53072arXivmath/0603350OpenAlexW2150941627MaRDI QIDQ2478595

Alan Weinstein, Xiang Tang, Eric Leichtnam

Publication date: 28 March 2008

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0603350

zbMATH Keywords

Poisson structure, pseudoconvexity, plurisubharmonic function, contact structure, Lie algebroid

Mathematics Subject Classification ID

Poisson manifolds; Poisson groupoids and algebroids (53D17) Deformation quantization, star products (53D55) Pluripotential theory (32U99)

Related Items (8)

On almost complex Lie algebroids ⋮ Asymptotic equivariant index of Toeplitz operators and relative index of CR structures ⋮ Deformation quantization with separation of variables of an endomorphism bundle ⋮ Helton-Howe trace, Connes-Chern characters and Toeplitz quantization of Bergman spaces ⋮ On the geometric quantization of contact manifolds ⋮ Infinitesimal deformations of a formal symplectic groupoid ⋮ Pre-symplectic algebroids and their applications ⋮ Star products with separation of variables admitting a smooth extension

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A relative index on the space of embeddable CR-structures. I
• Resolvent of the Laplacian on strictly pseudoconvex domains
• Toeplitz quantization of Kähler manifolds and \(gl(N)\), \(N\to \infty\) limits
• A simple geometrical construction of deformation quantization
• A duality property for complex Lie algebroids
• Weighted Bergman kernels and quantization
• Star products on compact pre-quantizable symplectic manifolds
• Deformation quantizations with separation of variables on a Kähler manifold
• Formality for Lie algebroids
• The canonical connection of a bi-Lagrangian manifold
• Identification of Berezin-Toeplitz deformation quantization
• Generalized Calabi-Yau Manifolds
• Transverse measures, the modular class and a cohomology pairing for Lie algebroids
• Lectures on symplectic geometry

This page was built for publication: Poisson geometry and deformation quantization near a strictly pseudoconvex boundary