The simplicial volume of 3-manifolds with boundary

We provide sharp lower bounds for the simplicial volume of compact $3$-manifolds in terms of the simplicial volume of their boundaries. As an application, we compute the simplicial volume of several classes of $3$-manifolds, including handlebodies and products of surfaces with the interval. Our results provide the first exact computation of the simplicial volume of a compact manifold whose boundary has positive simplicial volume. We also compute the minimal number of tetrahedra in a (loose) triangulation of the product of a surface with the interval.
Comment: 24 pages, 5 figures. Section 6 has been removed, and will appear in a separate paper by the same authors. This version has been accepted for publication by the Journal of Topology