Lectures on Integrability of Lie Brackets

Abstract

This is a set of lecture notes for a course given at the 2005 Summer School in Poisson Geometry held at ICTP-Trieste.

95 pages. To be published by Mathematical Sciences Publishers

References in corpus (3)

• Orbifolds as Groupoids: an Introduction
• Some title containing the words "homotopy" and "symplectic", e.g. this one
• Introduction to the language of stacks and gerbes

Cited by in corpus (47)

• Symplectic and Poisson geometry on b-manifolds
• BMS Particles in Three Dimensions
• Centrally extended BMS4 Lie algebroid
• Charge Algebra in Al(A)dS${}_n$ Spacetimes
• A note on gauge systems from the point of view of Lie algebroids
• Lie Algebroid Yang Mills with Matter Fields
• Connections on Lie algebroids and on derivation-based noncommutative geometry
• Poincaré--Birkhoff--Witt isomorphisms and Kapranov dg-manifolds
• Beyond the standard gauging: gauge symmetries of Dirac Sigma Models
• Relational symplectic groupoids and Poisson sigma models with boundary
• On the Various Extensions of the BMS Group
• Graded Bundles in the Category of Lie Groupoids
• Cartan Connections on Lie Groupoids and their Integrability
• On the Geometry of the Hamilton-Jacobi Equation and Generating Functions
• The Role of the Jacobi Identity in Solving the Maurer-Cartan Structure Equation
• Jacobi bundles and the BFV-complex
• Almost regular Poisson manifolds and their holonomy groupoids
• Van Est differentiation and integration
• Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators
• The Atiyah algebroid of the path fibration over a Lie group
• Homotopy momentum sections on multisymplectic manifolds
• Geometric structures and Lie algebroids
• Integration of singular foliations via paths
• Poisson manifolds and their associated stacks
• Integration of Coupling Dirac Structures
• A Lagrangian for Hamiltonian vector fields on singular Poisson manifolds
• Cartan geometries and multiplicative forms
• Grinberg-Kazhdan theorem and Newton groupoids
• The Infinitesimalization and Reconstruction of Locally Homogeneous Manifolds
• Integration of quadratic Lie algebroids to Riemannian Cartan-Lie groupoids
• Lie Algebroid Invariants for Subgeometry
• Deformations of symplectic groupoids
• The modular class of a Poisson map
• Gauge field theories: various mathematical approaches
• Pseudogroups via pseudoactions: Unifying local, global, and infinitesimal symmetry
• A Characterisation of Smooth Maps into a Homogeneous Space
• The Lie algebroid associated with a hypersurface
• Lie algebroids generated by cohomology operators
• Banach-Lie groupoids and generalized inversion
• Multiplicative Gray stability
• Local description of generalized forms on transitive Lie algebroids and applications
• The Classifying Lie Algebroid of a Geometric Structure I: Classes of Coframes
• Symplectic Foliations, Currents, and Local Lie Groupoids
• Cotangent Microbundle Category, I
• Notes on Geometric Morita equivalence of twisted Poisson manifolds
• Representation up to homotopy of Hom-Lie algebroids
• Proper Lie groupoids are real analytic