6 problems

Boidol's conjecture. Every symmetric locally compact group is $*$-regular, and conversely every almost connected, $*$-regular group is symmetric.

Finite Hirsch length conjecture. The group $G$ has finite Hirsch length if and only if

Let $G$ be a discrete, torsion-free, amenable group, and let $I(G)$ be the augmentation ideal, namely the kernel of the trivial representation $C^*(G)\to\mathbb{C}$. For a separabl…

Let $G$ be a locally compact group, and let $G_d$ denote the group $G$ endowed with the discrete topology. Write $C^*_{\lambda_G}(G_d)$ for the C-algebra associated with the left r…

Let $K(n)$ be the group associated with the continuous field of $C^*$-algebras constructed in the paper, let $A$ denote the corresponding $C^*$-algebra, and let $G(3,n)$ be the fre…

Let $M$ be a finite aspherical $CW$-complex (or weakly a closed, connected, oriented and aspherical Riemannian manifold) with fundamental group $\pi$. Write $C_{r}^{\ast }(\pi )$ f…