Equation 5.2.5B25865120DE7

\begin{equation} \mathrm{d}(\alpha \wedge \gamma )=\mathrm{d}\alpha \wedge \gamma +(-1)^ k\alpha \wedge \mathrm{d}\gamma , \qquad \mathrm{d}^2=0,\qquad F^*\mathrm d\alpha =\mathrm dF^*\alpha \end{equation}