Lectures on integrability of Lie brackets

By Rui Loja Fernandes, M. Crainic. 2006

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These notes are made up of five lectures. In Lecture 1, we introduce Lie groupoids and their infinitesimal versions. In Lecture 2, we introduce the abstract notion of a Lie algebroid and explain how many notions of differential geometry can be described in this language. Lectures 1 and 2 should help you in becoming familiar with the language of Lie groupoids and Lie algebroids. Lectures 3 and 4 are concerned with the various aspects of the integrability problem. These two lectures form the core material of this course and contain a detailed description of the integrability obstructions. In Lecture 5 we consider, as an example, aspects of integrability related to Poisson geometry. At

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

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