The simplicial volume of 3-manifolds with boundary

Abstract

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.

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

References in corpus (4)

• Layered-triangulations of 3-manifolds
• Stable complexity and simplicial volume of manifolds
• Isometric properties of relative bounded cohomology
• Simplicial volume and fillings of hyperbolic manifolds

Cited by in corpus (7)

• Stable complexity and simplicial volume of manifolds
• On minimal ideal triangulations of cusped hyperbolic 3-manifolds
• On the simplicial volume and the Euler characteristic of (aspherical) manifolds
• Ideal simplicial volume of manifolds with boundary
• Bounds for the genus of a normal surface
• Cubical simplicial volume of 3-manifolds
• Efficient cycles of hyperbolic manifolds