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

Abstract

Abstract For a group G, let ℱ n {\mathcal{F}_{n}} be the family of all subgroups of G containing a subgroup of finite index isomorphic to ℤ r {\mathbb{Z}^{r}} for some r = 0 , 1 , 2 , … , n {r=0,1,2,\dots,n} . Joecken, Lafont and Sánchez Saldaña computed the ℱ 1 {\mathcal{F}_{1}} -geometric dimension of 3-manifold groups. As a natural extension of the aforementioned result, the goal of this article is to compute the ℱ n {\mathcal{F}_{n}} -geometric dimension of 3-manifold groups for all n ≥ 2 {n\geq 2} .