10 problems

Let $G$ be a group, let $E_{\mathcal{VCY}}(G)$ be the classifying $G$-space for the family of virtually cyclic subgroups, and let $\mathcal{A}$ be an additive $G$-category with inv…

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…

Let $cGamma$ be a group, let ${cE}$ be a $cGamma$-space universal for virtually cyclic subgroups, and write ${cB}={cE}/cGamma$. For a space $X$ with a free, properly discontinuous…

Let $G$ and $F$ be groups, and define their wreath product by $G\wr F=(\prod_F G)\rtimes F$, with $F$ permuting the factors. The Full Farrell–Jones conjecture. A group $G$ satisfie…

Let $G$ be a group, let $R$ be a ring with involution, and let $\mathbf{L}^{\langle-\infty\rangle}(R)$ be the associated $L$-theory spectrum, whose $n$th homotopy group is…

Let $G$ be a group, let $R$ be a regular ring, and let $BG$ be a classifying space for $G$. The spectrum $\mathbf{K}(R)$ represents algebraic $K$-theory, and the assembly map is th…

Compact virtually cyclic Farrell–Jones conjecture. This assembly map is an equivalence. It is motivated by the discrete Farrell–Jones conjecture, with products retained in the inde…

Compact-open Farrell–Jones conjecture. This assembly map is an isomorphism for all $n$. This is the paper's main assembly statement for Hecke categories under (Reg); the supplied t…

Let ${\mathbf S}\colon\operatorname{SPACES}\to\operatorname{SPECTRA}$ be a covariant functor respecting weak equivalences and disjoint unions. Let $G$ be a group, ${\mathcal F}$ a…

Let ${\mathbf S} \colon \operatorname{SPACES}\to \operatorname{SPECTRA}$ be a covariant functor respecting weak equivalences and disjoint unions. For a group $G$, let…