5 problems

Let $X^n$ be a space and let $p$ be a prime. Say that $H^*(X;\mathbb{Z}_p)$ is $k$-periodic up to degree $c$ when multiplication by a periodicity element induces successive isomorp…

Let $X$ be a topological space and let $p$ be an odd prime. A nonzero element $x\in H^k(X;\mathbb{Z}_p)$ induces periodicity if multiplication by $x$ gives isomorphisms … for all…

Let $X$ be a connected topological space. A nonzero element $x\in H^k(X;\mathbb{Z}_2)$ induces periodicity if multiplication by $x$ gives isomorphisms … for all $i\geq 0$; in this…

Let $E_{b4}(Z)$ be the operator associated with the elliptic complex on the periodic end, and let $\widehat{H}^*_z(V)$ denote the corresponding periodic cohomology group, with para…

Let $\Gamma$ be a group. Its cohomological dimension is … The group $\Gamma$ has periodic cohomology after $k$ steps if there exists an integer $q>0$ such that $H^i(\Gamma,-)$ and…