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The Geometry of Physics by Theodore Frankel

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CHAPTER 17

Fiber Bundles, Gauss–Bonnet, and Topological Quantization

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A vector bundle is a family of vector spaces parameterized by points in the base space. How do we parameterize a family of manifolds, say Lie groups?

17.1. Fiber Bundles and Principal Bundles

17.1a. Fiber Bundles

The tangent bundle TMn to a Riemannian manifold is a vector bundle associated to M; it is locally of the form U × imagen .We have had occasion also to consider the set of unit vectors tangent to M; that is, we may consider, in each fiber π−1(p) ≈ n of TM (a vector space ...

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