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AN INTRODUCTION TO DIFFERENTIAL MANIFOLDS
by Dennis Barden & Charles Thomas (University of Cambridge, UK)
This invaluable book, based on the many years of teaching experience of both authors, introduces the reader to the basic ideas in differential topology. Among the topics covered are smooth manifolds and maps, the structure of the tangent bundle and its associates, the calculation of real cohomology groups using differential forms (de Rham theory), and applications such as the Poincaré–Hopf theorem relating the Euler number of a manifold and the index of a vector field. Each chapter contains exercises of varying difficulty for which solutions are provided. Special features include examples drawn from geometric manifolds in dimension 3 and Brieskorn varieties in dimensions 5 and 7, as well as detailed calculations for the cohomology groups of spheres and tori.
Contents:
- Differential Manifolds and Differentiable Maps
- The Derivatives of
Differentiable Maps
- Fibre Bundles
- Differential Forms and Integration
- The Exterior Derivative
- De Rham Cohomology
- Degrees, Indices and Related Topics
- Lie Groups
- A Rapid Course in Differential Analysis
Readership: Upper level undergraduates, beginning graduate students, and
lecturers in geometry and topology.
"This book is an excellent introductory text into the theory of differential manifolds with a carefully thought out and tested structure and a sufficient supply of exercises and their solutions. It does not only guide the reader gently into the depths of the theory of differential manifolds but also careful on giving advice how one can place the information in the right context. It is certainly written in the best traditions of great Cambridge mathematics."
| Acta Scientiarum Mathematicarum |
| 232pp |
Pub. date: Mar 2003 |
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