de Rham theorem

《一般拓扑学基础》 · 第 396 页 · footnote 1

If \(\Omega^*(X)\) is the de Rham complex of a differentiable manifold, de Rham's theorem gives \(H^p(\Omega^*(X))\cong H^p(X;\mathbb R)\), and \([\omega]\smile[\omega']=[\omega\wedge\omega']\).