Let $X$ be a $C^\infty$ manifold, compact oriented and connected of dimension $n$. How do you prove that the integration map $$\int_X: \omega \mapsto \int_X \omega $$ from $H^n_{DR}(X)$ to $\mathbb{R}$ is an isomorphism? (Without using Poincare duality).
Highest DeRahm Cohomology
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algebraic-topology
differential-topology
manifolds
homology-cohomology
differential-forms