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 Poincare-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.
- ISBN13 9781860943546
- Publish Date 13 March 2003
- Publish Status Active
- Publish Country GB
- Imprint Imperial College Press
- Format Hardcover
- Pages 232
- Language English
- URL https://worldscientific.com/worldscibooks/10.1142/p285