Pontryagin ring of an odd-sphere loop space
= Pontryagin ring of an odd-sphere loop space
{c}
{title2=$H_*(\Omega S^{2n+1};\mathbb Z)=\mathbb Z[x_{2n}]$}
For $n\geq1$, the <Bott–Samelson theorem> gives a single homology generator of degree $2n$ with no word relations. Its <Pontryagin product> satisfies $x^i*x^j=x^{i+j}$. Unlike this polynomial <homology> product, the <cohomology> cup product has divided-power coefficients.