ENGLISH

Topological geometry

By Ian R. Porteous

Book information

Publisher
Cambridge University Press
Year
1981
ISBN
9780521231602, 9780521298391, 0521231604, 0521298393
LCC
QA564 .P66 1981
Open Library ID
OL4425834M
Language
english
Format
DJVU
Filesize
3 MB (3036687 bytes)
Edition
2nd
Pages
495\495
Library
Kolxo3
DPI
300
Time added
2010-07-29 05:14:56

Description

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.

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