Cohomology suspension
= Cohomology suspension
{title2=$\sigma:\widetilde H^q(B;R)\to\widetilde H^{q-1}(\Omega B;R)$}
Pull back along loop evaluation $S^1\times\Omega B\to B$ and take the slant product with the circle's fundamental class. This degree-lowering operation kills positive-degree cup products. It commutes with stable <cohomology> operations such as <Steenrod squares> and identifies a transgressing base class with its fiber class in the path-loop fibration.