= Chern-Weil connection transgression
{c}
{title2=$\partial_t\operatorname{Tr}F_t^2=2d\operatorname{Tr}(\dot A_t\wedge F_t)$}
A variation of the <connection one-form> has $\dot F=D_A\dot A$. The <Bianchi identity> and graded cyclic <matrix trace> imply $\partial_t\operatorname{Tr}(F\wedge F)=2d\operatorname{Tr}(\dot A\wedge F)$. Thus the <Chern-Weil theory> four-form changes by an <exact differential form>, and its integral on a closed four-cycle is connection-independent. For a general unitary bundle, include the corresponding trace-product term in the <Second Chern form>.
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