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Lie groupoids and Lie algebroids in differential geometry /
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 L...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge [Cambridgeshire] ; New York :
Cambridge University Press,
1987.
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| Colección: | London Mathematical Society lecture note series ;
124. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title; Copyright; Contents; Introduction; Dedication; CHAPTER I The algebra of groupoids; Introduction; 1. Groupoids; 2. Morphisms, subgroupoids and quotient groupoids; 3. Transitive and totally intransitive groupoids; CHAPTER II Topological groupoids; Introduction; 1. Basic definitions and examples; 2. Local triviality; 3. Components in topological groupoids; 4. Representations of topological groupoids; 5. Admissible sections; 6. The monodromy groupoid of a locally trivial groupoid; 7. Path connections in topological groupoids; CHAPTER III Lie groupoids and Lie algebroids
- Introduction1. Differentiable and Lie groupoids; 2. Lie algebroids; 3. The Lie algebroid of a differentiable groupoid; 4. The exponential map and adjoint formulas; 5. Infinitesimal connection theory and the concept of transition form; 6. The Lie theory of Lie groupoids over a fixed base; 7. Path connections in Lie groupoids; CHAPTER IV The cohomology of Lie algebroids; Introduction; 1. The abstract theory of transitive Lie algebroids; 2. The cohomology of Lie algebroids; 3. Non-abelian extensions of Lie algebroids and the existence of transitive Lie algebroids with prescribed curvature
- 4. The existence of local flat connections and families of transition forms5. The spectral sequence of a transitive Lie algebroid; CHAPTER V An obstruction to the Integrability of transitive Lie algebroids; Introduction; 1. Results; 2. Epilogue; APPENDIX A On principal bundles and Atiyah sequences; Introduction; 1. Principal and fibre bundles; 2. Quotients of vector bundles over group actions; 3. The Atiyah sequence of a principal bundle; 4. Infinitesimal connections and curvature; APPENDIX B On Lie groups and Lie algebras; Introduction; 1. Definitions and notations
- 2. Formulas for the right derivativeAPPENDIX C On vector bundles; REFERENCES; INDEX