The simplicial volume of 3-manifolds with boundary

M. Bucher; R. Frigerio; C. Pagliantini

doi:10.1112/jtopol/jtv001

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arXiv · 1208.0545

The simplicial volume of 3-manifolds with boundary

M. Bucher·R. Frigerio·C. Pagliantini

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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.

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BibTeX RIS

M. Bucher, R. Frigerio, C. Pagliantini. 2012-08-02. The simplicial volume of 3-manifolds with boundary. https://doi.org/10.1112/jtopol%2Fjtv001

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