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Chapter 2 Lie Groups and Vector Bundles

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Abstract

A (differentiable) vector bundleof rank nconsists of a total space E,a base M,and a projection π :E → M,where Eand Mare differentiable manifolds, πis differentiable, each “fiber” Ex:= π -1(x) for x Є M,carries the structure of an n-dimensional (real) vector space, and the following local triviality requirement is satisfied: For each x Є M,there exist a neighborhood Uand a diffeomorphism.

Keywords

  • Riemannian Manifold
  • Vector Bundle
  • Tangent Bundle
  • Spin Structure
  • Integral Curf

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  • DOI: 10.1007/978-3-642-21298-7_2
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Correspondence to Jürgen Jost .

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© 2011 Springer-Verlag Berlin Heidelberg

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Jost, J. (2011). Chapter 2 Lie Groups and Vector Bundles. In: Riemannian Geometry and Geometric Analysis. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21298-7_2

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