6 problems

Let $G$ be a torsion-free group. Say that $G$ has periodic cohomology after $k$ steps over $R$ if there is an integer $q\geq 0$ such that the functors $H^i_R(G,-)$ and…

Let $G$ be a torsion-free group that acts freely and properly discontinuously on some $S^n\times \mathbb{R}^k$. Talelli's conjecture. $G$ can act freely and properly discontinuousl…

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…