By (author) Ian R. Porteous
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Topological Geometry by Ian R. Porteous
Book DescriptionThe 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.
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Book DetailsISBN: 9780521298391
(228mm x 152mm x 28mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 5-Feb-1981
Country of Publication: United Kingdom
Books By Author Ian R. Porteous
Clifford Algebras and the Classical Groups, Paperback (August 2009)
A treatment of the theory of Clifford algebras that will be welcomed for its clarity and detail.
Geometric Differentiation, Hardback (December 2001)» View all books by Ian R. Porteous
This is a revised version of the popular Geometric Differentiation, first edition.
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