Topological Geometry / Edition 2

by Ian R. Porteous

Overview

The earlier chapter of this self-contained text provide a route from first principles through standard linear and quadratic algebra to geometric algebra, with Clifford's geometric algebras taking pride of place. In parallel with this is an account, also from first principles, of the elementary theory of topological spaces and of continuous and differentiable maps that leads up to the definitions of smooth manifolds and their tangent spaces and of Lie groups and Lie algebras. The calculus is presented as far as possible in basis free form to emphasize its geometrical flavour and its linear algebra content. In this second edition Dr Porteous has taken the opportunity to add a chapter on triality which extends earlier work on the Spin groups in the chapter on Clifford algebras. The details include a number of important transitive group actions and a description of one of the exceptional Lie groups, the group G2. A number of corrections and improvements have also been made. There are many exercises throughout the book and senior undergraduates in mathematics as well as first-year graduate students will continue to find it stimulating and rewarding.

Product Details

ISBN-13:	9780521298391
Publisher:	Cambridge University Press
Publication date:	02/05/1981
Edition description:	Second Edition
Pages:	500
Product dimensions:	5.98(w) x 8.98(h) x 1.06(d)

Table of Contents

Foreword; Guide; 1. Maps; 2. Real and complex numbers; 3. Linear spaces; 4. Affine spaces; 5. Quotient structures; 6. Finite-dimensional spaces; 7. Determinants; 8. Direct sum; 9. Orthogonal spaces; 10. Quaternions; 11. Correlations; 12. Quadric Grassmannians; 13. Clifford Algebras; 14. The Cayley algebra; 15. Normed linear spaces; 16. Topological spaces; 17. Topological groups and manifolds; 18. Affine approximation; 19. The inverse function theorem; 20. Smooth manifolds; 21. Triality; Bibliography; List of symbols; Index.

Editorial Reviews

Review of the hardback: '… a remarkable book, which is likely to remain very useful, both for teaching and research, during many years to come.' J.Dieudonné in Zentralblatt Für Mathematik

From the Publisher