Poisson geometry and Morita equivalence
arXiv:math/0402347
Abstract
These notes discuss various aspect of the ``representation theory'' of Poisson manifolds, with focus on Morita equivalence and Picard groups. We give a brief introduction to Poisson geometry (including Dirac and twisted Poisson structures) and algebraic Morita theory before presenting the geometric Morita theory of Poisson manifolds. We also point out the connections with the theory of symplectic groupoids and hamiltonian actions.
52 pages. Expanded notes from the mini-course taught by A. Weinstein at the PQR 2003 Euroschool in Brussels. Revised version, to appear in the London Math.Society Lecture Notes series
References in corpus (11)
- Deformation quantization of Poisson manifolds, I
- Morita equivalence and duality
- WZW-Poisson manifolds
- Some title containing the words "homotopy" and "symplectic", e.g. this one
- Topological and Smooth Stacks
- The characteristic classes of Morita equivalent star products on symplectic manifolds
- On the integration of Poisson manifolds, Lie algebroids, and coisotropic submanifolds
- Picard groups in Poisson geometry
- Semiclassical Geometry of Quantum Line Bundles and Morita Equivalence of Star Products
- Completely positive inner products and strong Morita equivalence
- Linearization of Poisson brackets
Cited by in corpus (15)
- Integrating Poisson manifolds via stacks
- Regular Poisson manifolds of compact types (PMCT 2)
- Lie algebroids, Lie groupoids and TFT
- On holomorphic maps and Generalized Complex Geometry
- Formality and Star Products
- Brane quantization of toric Poisson varieties
- Principal actions of stacky Lie groupoids
- Convergence of Star Product: From Examples to a General Framework
- On the integrability of subalgebroids
- On the developability of subalgebroids
- Deformations of anti-de Sitter black holes
- Equivalence of the categories of modules over Lie algebroids
- Defects in Spin Chains via Cluster Categories
- Notes on Geometric Morita equivalence of twisted Poisson manifolds
- Geometric quantization of Dirac manifolds