9 problems

Let $G$ be a torsion-free group and let $R$ be a regular ring. Farrell–Jones conjecture for $K_0$. The map induced by the inclusion $R\to RG$ is an isomorphism … This is described…

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

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-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…

A-theoretic Farrell--Jones conjecture. The assembly map

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…