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The Geometry of Physics by Theodore Frankel

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CHAPTER 22

Chern Forms and Homotopy Groups

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How can we construct closed p-forms from the matrix θ2 of curvature forms?

22.1. Chern Forms and Winding Numbers

22.1a. The Yang–Mills “Winding Number”

Recall that in (20.62) and (20.63), we were comparing, on a distant 3-sphere S3image4, the interior frame eU with the covariant constant frame eV,

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the gauge group being assumed SU (n).

We saw in (21.14) that the Cartan 3-form on SU (n)

is a nontrivial ...

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