5 problems

Let $\Gamma$ be a discrete subgroup of a Lie group that is not virtually cyclic. Write $vcd(\Gamma)$ for its virtual cohomological dimension, and let $B_{\mathcal{VC}}\Gamma$ denot…

Vanishing upper Serre dimension conjecture. The upper Serre dimension satisfies

Rationality and nonnegativity conjecture. The two Serre dimensions are rational numbers, and the upper Serre dimension is nonnegative:

Local-freeness conjecture. Every group $G$ satisfying

Let $G$ be an elementary amenable group and let $k$ be a non-zero commutative ring. The homological dimension–Hirsch length conjecture. If $G$ has no $k$-torsion, then … Equivalent…