Poincare 1893: closed orientable n-manifold M has H^k(M) iso H_(n-k)(M) iso H^(n-k)(M); intersection-pairing nondegenerate on H^k x H^(n-k); foundation of intersection theory.
Poincare 1893: closed orientable n-manifold M has H^k(M) iso H_(n-k)(M) iso H^(n-k)(M); intersection-pairing nondegenerate on H^k x H^(n-k); foundation of intersection theory.