Chern-Weil theory

Chern-Weil theory constructs closed characteristic forms by applying invariant polynomials to the curvature of a connection.

Table of contents
- Second Chern form Chern-Weil theory
  - Chern-Simons 3-form Second Chern form

Second Chern form

For curvature

F = d A + A \land A

, a standard normalization of the second Chern form is

C_{2} = \frac{1}{8 π ^{2}} Tr (F \land F) .

Chern-Simons 3-form

The Chern-Simons 3-form

Y = \frac{1}{8 π ^{2}} Tr (A \land d A + \frac{2}{3} A \land A \land A)

satisfies

d Y = C_{2}

.

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