Sutured manifolds and ℓ2-Betti numbers

Abstract

Using the virtual fibering theorem of Agol, we show that a sutured 3-manifold (M, R+, R_, ?) is taut if and only if the l(2)-Betti numbers of the pair (M, R_) are zero. As an application, we can characterize Thurston norm minimizing surfaces in a 3-manifold N with empty or toroidal boundary by the vanishing of certain l(2)-Betti numbers.