The simplicial volume of 3-manifolds with boundary
Geometric Topology
2015-06-12 v3 Algebraic Topology
Differential Geometry
Abstract
We provide sharp lower bounds for the simplicial volume of compact -manifolds in terms of the simplicial volume of their boundaries. As an application, we compute the simplicial volume of several classes of -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.
Keywords
Cite
@article{arxiv.1208.0545,
title = {The simplicial volume of 3-manifolds with boundary},
author = {M. Bucher and R. Frigerio and C. Pagliantini},
journal= {arXiv preprint arXiv:1208.0545},
year = {2015}
}
Comments
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