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For a group $G$, let $\mathcal{F}_{n}$ be the family of all the subgroups of$G$ containing a subgroup isomorphic to $\mathbb{Z}^{r}$ for some$r=0,1,2,\dots ,n$ of finite index. Joecken, Lafont and S\'anchez Salda\~nacomputed the $\mathcal{F}_1$-dimension of 3-manifold groups. The goal of thisarticle is to compute the $\mathcal{F}_n$-geometric dimension of 3-manifoldgroups for all $n\geq 2$.

Classifying spaces for the family of virtually abelian subgroups of orientable $3$-manifold groups