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The Geometry of Physics by Theodore Frankel

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CHAPTER 16

Vector Bundles in Geometry and Physics

image

 

On the Earth’s surface, the number of peaks minus the number of passes plus the number of pits is generically 2.

16.1. Vector Bundles

What is a “twisted product”?

16.1a. Motivation by Two Examples

1. Vector fields on M. A section of the tangent bundle TMn to Mn is simply a vector field w on M. Locally, that is, in a coordinate patch (U; u1,…, un), w is given by its component functions image with respect to the coordinate basis ∂/∂u, but of course these functions are defined only on U, not all of ...

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