Sutured manifolds and ℓ2-Betti numbers

Abstract

Abstract Using the virtual fibering theorem of Agol, we show that a sutured 3-manifold $(M, R_{+},R_{-},\gamma)$ is taut if and only if the $\ell^{2}$-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 $\ell^{2}$-Betti numbers.