9 problems

A group of type $F$ is torsion-free, and the Whitehead group $\operatorname{Wh}(G)$ is the obstruction to making the $L^2$-torsion polytope of $G$ well-defined in the stated constr…

Relative $L$-theory identification. There is a natural identification

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…

Whitehead-group conjecture. The group $W(G,K)$ is abelian. If so, it has finite exponent depending only on the type of $G$. The conjecture has been established in many cases, while…

Let $G$ be a group, let $\mathcal{FC}\!\mathit{yc}$ be the family of finite cyclic subgroups, let $(\mathcal{FC}\!\mathit{yc})$ denote their conjugacy classes, let $Z_GC$ be the ce…

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…

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 $k$ be a field and let $G$ be the reductive group considered in the paper. For every finitely generated extension $L/k$, let $W(L,G)$ denote the corresponding Whitehead group.…

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…