Riemann-Roch theorems via deformation quantization. I

DOI10.1006/aima.2000.1977zbMath1021.53064arXivalg-geom/9705014OpenAlexW4213154823MaRDI QIDQ1604333

Paul Bressler, Boris Tsygan, Ryszard Nest

Publication date: 4 July 2002

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/alg-geom/9705014

zbMATH Keywords

Chern charactercomplex manifold\(D\)-modulemicrolocal Euler classsymplectic deformation quantization

Mathematics Subject Classification ID

Index theory and related fixed-point theorems on manifolds (58J20) Sheaves of differential operators and their modules, (D)-modules (32C38) Deformation quantization, star products (53D55) Relations of PDEs on manifolds with hyperfunctions (58J15)

Related Items (20)

Modules over deformation quantization algebroids: An overview ⋮ Oscillatory modules ⋮ Geometry of localized effective theories, exact semi-classical approximation and the algebraic index ⋮ Hochschild Lefschetz class for \(\mathcal D\)-modules ⋮ Deformations of algebroid stacks ⋮ Derived moduli of complexes and derived Grassmannians ⋮ Chern characters and Hirzebruch-Riemann-Roch formula for matrix factorizations ⋮ A variant of the Mukai pairing via deformation quantization ⋮ Index theory and noncommutative geometry: a survey ⋮ The algebraic index theorem and deformation quantization of Lagrange-Finsler and Einstein spaces ⋮ Cyclic cocycles on deformation quantizations and higher index theorems ⋮ Microlocal Euler classes and Hochschild homology ⋮ Riemann–Roch for Real Varieties ⋮ Derived geometry of the first formal neighbourhood of a smooth analytic cycle ⋮ One-dimensional Chern-Simons theory and the \(\widehat{A}\) genus ⋮ Formality and Kontsevich-Duflo type theorems for Lie pairs ⋮ An algebraic index theorem for Poisson manifolds ⋮ EQUIVARIANT ALGEBRAIC INDEX THEOREM ⋮ Riemann-Roch theorems via deformation quantization. II ⋮ A formality theorem for Hochschild chains.

Cites Work

• Cohomologies of Lie algebras of generalized Jacobi matrices
• Deformation theory and quantization. II: Physical applications
• Algebraic index theorem
• Deformations of the algebra of functions of a symplectic manifold. Comparison between Fedosov and de Wilde, Lecomte
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