= Periodic group cohomology
{title2=$\Delta\smile-:H^i(G;M)\cong H^{i+n}(G;M)$}
For a finite group, the usual integral notion asks for a class $\Delta\in H^n(G;\mathbb Z)$ whose <cup product> gives the displayed isomorphisms for every coefficient module $M$ and every $i>0$. The analogous claim for just trivial coefficients over a fixed field is weaker and should be stated as such. A free cohomologically orientation-preserving sphere action supplies that field-coefficient version through <periodic group cohomology from a free sphere action>.
Back to article page
