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).
KeywordsVector Field Quadratic Form Fibre Bundle Clifford Algebra Irreducible Module
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