Abstract: We will revisit two important operations on differential forms, namely, contraction and Lie derivative. In particular, if M is a $G$-manifold, then contraction and Lie derivative (both with respect to the fundamental vector fields), make the de Rham complex $\Omega(M)$ a $\mathfrak{g}$-DGA. Next, we will return to the Weil model for circle actions and show that it is isomorphic to the polynomial ring with circle-invariant forms on $M$ as the coefficients.

Meeting ID: 997 4840 9440 Passcode: 911104