Homology cross product (source code)

= Homology cross product
{title2=$H_p(X)\otimes H_q(Y)\to H_{p+q}(X\times Y)$}

The singular-chain product induces this natural pairing on <homology>. Composing it with multiplication of a loop space gives the <Pontryagin product on loop-space homology>. This is different from the vector <cross product>.