## Abstract

The treewidth of a 3-manifold triangulation plays an important role in algorithmic 3-manifold theory, and so it is useful to find bounds on the treewidth in terms of other properties of the manifold. We prove that there exists a universal constant c such that any closed hyperbolic 3-manifold admits a triangulation of treewidth at most the product of c and the volume. The converse is not true: we show there exists a sequence of hyperbolic 3-manifolds of bounded treewidth but volume approaching infinity. Along the way, we prove that crushing a normal surface in a triangulation does not increase the carving-width, and hence crushing any number of normal surfaces in a triangulation affects treewidth by at most a constant multiple.

Original language | English |
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Pages (from-to) | 2625-2652 |

Number of pages | 28 |

Journal | Algebraic and Geometric Topology |

Volume | 19 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1 Jan 2019 |

## Keywords

- 3-Manifold triangulation
- Crushing normal surface
- Hyperbolic volume
- Treewidth