4 problems

Let $G$ be a group and let $\mathcal C$ be a class of subgroups of $G$. There is a $G$-CW complex $E_{\mathcal C}(G)$ whose fixed-point set is contractible for subgroups in…

Let $G$ be a group and let $\mathcal H^G_*$ be one of the theories under consideration, with $E_{\mathcal{VC}}(G)$ denoting the classifying $G$-CW complex for virtually cyclic subg…

Let $G$ be a discrete group and let $W$ be a connected $G$-CW-complex with free $G$-action. Write ${\mathbb {A}}^{-\infty}(W)$ for the non-connective delooping of Waldhausen's alge…

The surgery-theoretic Fibered Isomorphism Conjecture. The assembly map in $L^{\langle -\infty\rangle}$-theory should be an isomorphism.