4 problems

Let $\mathcal P$ be the polynomial bounding class, and let $\mathbb{Z}[\mathbb{N}]$ denote the weighted free $\mathbb{Z}$-module on the weighted set $\mathbb{N}$. Consider the chai…

Let $G$ be the solvable group described in the source, with $BG$ homotopy equivalent to a closed oriented $3$-manifold, and let $E G$ be the homogeneous bar resolution. Let…

Let $M^3$ be the closed $3$-dimensional solvmanifold described in the source, let $\pi=\pi_1M^3$, and let $\mathcal P$ be the bounding class of polynomial functions. Let $E\pi$ be…

Let $\mathcal B$ be a bounding class, let $G$ be a group of type $\operatorname{FL}$, and let $EG$ be the homogeneous bar resolution of $G$. Write $\chi(G)$ for the Euler character…