Overview
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.
Full Product Details
Author: Dennis Barden (Univ Of Cambridge, Uk) ,
Charles B Thomas (Univ Of Cambridge, Uk)
Publisher: Imperial College Press
Imprint: Imperial College Press
Dimensions:
Width: 16.00cm
, Height: 0.90cm
, Length: 23.00cm
Weight: 0.349kg
ISBN: 9781860943553
ISBN 10: 1860943551
Pages: 232
Publication Date: 13 March 2003
Audience:
College/higher education
,
Professional and scholarly
,
Undergraduate
,
Postgraduate, Research & Scholarly
Format: Paperback
Publisher's Status: Active
Availability: In Print
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Reviews
""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
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
"""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"
