Mod-two Poincare duality
= Mod-two Poincare duality
{title2=$H_k(M;\mathbb F_2)\cong H^{n-k}(M;\mathbb F_2)$}
For a closed $n$-dimensional <manifold>, <Poincare duality> holds over $\mathbb F_2$ without an <orientation> assumption. The mod-two <fundamental class> exists because orientation signs disappear. The resulting complementary-degree <intersection pairing> is a <perfect pairing>.