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.
Not yet reviewed
Be the first to review
Review was not posted due to profanity×
- Date Published: June 1987
- format: Paperback
- isbn: 9780521348829
- length: 344 pages
- dimensions: 228 x 152 x 21 mm
- weight: 0.544kg
- availability: Available
Table of Contents
1. The algebra of groupoids
2. Topological groupoids
3. Lie groupoids and Lie algebroids
4. The cohomology of Lie algebroids
5. An obstruction to the integrability of transitive Lie algebroids
Appendix A: On principal bundles and Atiyah sequences
Appendix B: On Lie groups and Lie algebras
Appendix C: On vector bundles
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email email@example.comRegister Sign in
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.Continue ×
Are you sure you want to delete your account?
This cannot be undone.
Thank you for your feedback which will help us improve our service.
If you requested a response, we will make sure to get back to you shortly.×