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  3. Lie Groupoids and Lie Algebroids in Differential Geometry
  • Cited by 231
Publisher:
Cambridge University Press
Online publication date:
May 2010
Print publication year:
1987
Online ISBN:
9780511661839
DOI:
https://doi.org/10.1017/CBO9780511661839
Subjects:
Mathematics (general), Mathematics, Algebra
Series:
London Mathematical Society Lecture Note Series (124)
Information

Book description

This book provides a striking synthesis of the standard theory of connections in principal bundles and the Lie theory of Lie groupoids. The concept of Lie groupoid is a little-known formulation of the concept of principal bundle and corresponding to the Lie algebra of a Lie group is the concept of Lie algebroid: in principal bundle terms this is the Atiyah sequence. The author's viewpoint is that certain deep problems in connection theory are best addressed by groupoid and Lie algebroid methods. After preliminary chapters on topological groupoids, the author gives the first unified and detailed account of the theory of Lie groupoids and Lie algebroids. He then applies this theory to the cohomology of Lie algebroids, re-interpreting connection theory in cohomological terms, and giving criteria for the existence of (not necessarily Riemannian) connections with prescribed curvature form. This material, presented in the last two chapters, is work of the author published here for the first time. This book will be of interest to differential geometers working in general connection theory and to researchers in theoretical physics and other fields who make use of connection theory.

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