Abstract
Using methods from the theory of quadratic forms, one is able to construct vector bundles over spheres and projective spaces. We develop some general properties of Clifford algebras and completely calculate the Clifford algebras that arise in topology. Apart from constructing vector fields on a sphere, the topological applications are left to later chapters. Using Clifford algebras, we can give a concrete description of Spin(n).
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© 1994 Springer Science+Business Media New York
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Husemoller, D. (1994). Clifford Algebras. In: Fibre Bundles. Graduate Texts in Mathematics, vol 20. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2261-1_12
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DOI: https://doi.org/10.1007/978-1-4757-2261-1_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-2263-5
Online ISBN: 978-1-4757-2261-1
eBook Packages: Springer Book Archive