On quantum de Rham cohomology theory

DOI10.1090/S1079-6762-99-00056-6zbMath0926.53033arXivmath/9804145OpenAlexW1641796838MaRDI QIDQ4252958

Huai-Dong Cao, Jian Zhou

Publication date: 23 June 1999

Published in: Electronic Research Announcements of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9804145

zbMATH Keywords

deformation quantizationPoisson manifoldquantum curvaturequantum integralquantum de Rham cohomologyquantum characteristic classquantum Dolbeault cohomologyquantum exterior differentialquantum hard Lefschetz theoremquantum Stokes theorem

Mathematics Subject Classification ID

Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Poisson manifolds; Poisson groupoids and algebroids (53D17) Global theory of symplectic and contact manifolds (53D35) Geometric quantization (53D50)

Cites Work

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• Existence of star-products and of formal deformations of the Poisson Lie algebra of arbitrary symplectic manifolds
• A differential complex for Poisson manifolds
• Deformation theory and quantization. II: Physical applications
• Lectures on the geometry of Poisson manifolds
• A simple geometrical construction of deformation quantization
• Deformation quantization of Poisson manifolds
• Harmonic cohomology classes of symplectic manifolds
• Hodge structure on symplectic manifolds

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