An Introduction to Differential Manifolds
An Introduction to Differential Manifolds
ISBN: 9781860943553
出版社: World Scientific Pub Co Inc
出版年: 2003-3
页数: 232
定价: 421.00元
装帧: Pap
内容简介
An introduction to basic ideas in differential topology, based on the many years of teaching experience of both authors. 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.