4 problems

Structure-set rank conjecture. The free ranks satisfy

Finite-part assembly conjecture. The group $\widetilde{\mathcal M}_{\gamma_1,\ldots,\gamma_n}$ has rank $n$, and every nonzero element of $K_0^{\mathrm{fin}}(C^*(\Gamma))$ lies out…

Let $G$ be a group with torsion elements $g_1,g_2,\ldots,g_k$ of distinct positive orders $d_1,\ldots,d_k$. For each $g_i$, let $p_i$ be the idempotent corresponding to $g_i$, and…

Let $G$ be a countable group. For an element $g\in G$ of finite order $d$, define … in $\mathbb{Q}G$, and let $K_0^{\mathrm{fin}}(C^*(G))$ be the subgroup of $K_0(C^*(G))$ generate…