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Topological Geometry

£69.00

  • Date Published: February 1981
  • availability: Available
  • format: Paperback
  • isbn: 9780521298391

£ 69.00
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  • 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.

    Reviews & endorsements

    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

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    Product details

    • Date Published: February 1981
    • format: Paperback
    • isbn: 9780521298391
    • length: 500 pages
    • dimensions: 228 x 152 x 27 mm
    • weight: 0.73kg
    • availability: Available
  • 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.

  • Author

    Ian R. Porteous

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