Intersection Form (4-manifold) - Non-orientable Manifolds

Non-orientable Manifolds

Just as there is a version of Poincare duality for Z/2Z coefficients, there is also a version of the intersection form with Z/2Z coefficients, taking values in Z/2Z rather than in Z. In this way non-orientable manifolds get an intersection form as well. Of course one does not see any of this in de Rham cohomology.