5 problems

Let $X$ be a 4-manifold. The involution on $\operatorname{Wh}_1(\pi_1 X;\mathbb{Z}_2\times\pi_2 X)$ is induced by the involution on $(\mathbb{Z}_2\times\pi_2 X)[\pi_1 X]$, and let…

For a group $G$, let $\operatorname{Wh}(G)$ denote its Whitehead group, and let $\mathcal{F}\!\mathit{in}$ be the family of finite subgroups. The rational Whitehead injectivity con…

For a group $G$, the Whitehead group $\operatorname{Wh}(G)$ is the quotient of $K_1(\mathbb{Z}[G])$ by the subgroup represented by the units $\pm g$ for $g\in G$. The Whitehead van…

Let $M$ be a closed, connected, smooth manifold of dimension at least $5$ with torsion-free fundamental group. An $h$-cobordism over $M$ is a smooth cobordism over $M$ for which bo…

Let $p$ be an odd prime and let $i$ be a positive integer. For $n\geq 2i$, define … where $E(i)$ is $1$ if $i$ is even and $0$ if it is odd. Let…