4 problems

Let $G$ be a group and let $\operatorname{Wh}(G)$ denote its Whitehead group. The Whitehead group conjecture. If $G$ is torsionfree, then $\operatorname{Wh}(G)$ vanishes. This woul…

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…

Vanishing conjecture for the Whitehead group. The Whitehead group of a torsionfree group vanishes.