5 problems

Let $G$ be a torsion-free group, and let $\operatorname{Wh}(G)$ denote its Whitehead group. Whitehead conjecture. The Whitehead group of any torsion-free group should vanish: … Thi…

Cohen's conjecture. If $\tau\neq 0$, then the injection $G\to\widehat G$ cannot be onto.

Cohen's conjecture. For every group $\pi$,

Higher Whitehead torsion and Reidemeister trace compatibility conjecture. The following diagram commutes up to natural homotopy:

Let $L_1$ and $L_2$ be exact Lagrangians with Floer homology $HF(L_1,L_2)$ and Floer complex $CF(L_1,L_2)$, whose Whitehead torsion is denoted by $\tau(CF(L_1,L_2))$. Fukaya's conj…