The equivariant IP assembly-map conjecture

Let $\Gamma$ be a countable group acting properly and isometrically on the Euclidean space $\mathbb{E}_{\Gamma}$, and let $\mu_{\mathrm{IP}}$ denote the assembly map for the equivariant IP-cohomology theory. Equivariant IP assembly-map conjecture. The assembly map is a $\Gamma$-weak equivalence.

This conjecture is proposed as an analogue of the Baum–Connes and Farrell–Jones conjectures for the equivariant IP-cohomology theory. The paper establishes comparisons with localization and Davis–Lück assembly maps, but the asserted equivalence remains conjectural.