The triangulation complexity of fibred 3-manifolds

Fuente: arXiv
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Main Authors: Lackenby, Marc, Purcell, Jessica S.
Format: Preprint
Published: 2019
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author Lackenby, Marc
Purcell, Jessica S.
author_facet Lackenby, Marc
Purcell, Jessica S.
contents The triangulation complexity of a closed orientable 3-manifold is the minimal number of tetrahedra in any triangulation of the manifold. The main theorem of the paper gives upper and lower bounds on the triangulation complexity of any closed orientable hyperbolic 3-manifold that fibres over the circle. We show that the triangulation complexity of the manifold is equal to the translation length of the monodromy action on the mapping class group of the fibre, up to a bounded factor, where the bound depends only on the genus of the fibre.
format Preprint
id arxiv_https___arxiv_org_abs_1910_10914
institution arXiv
publishDate 2019
record_format arxiv
spellingShingle The triangulation complexity of fibred 3-manifolds
Lackenby, Marc
Purcell, Jessica S.
Geometric Topology
57Q15, 57N10, 57M50, 57M27
The triangulation complexity of a closed orientable 3-manifold is the minimal number of tetrahedra in any triangulation of the manifold. The main theorem of the paper gives upper and lower bounds on the triangulation complexity of any closed orientable hyperbolic 3-manifold that fibres over the circle. We show that the triangulation complexity of the manifold is equal to the translation length of the monodromy action on the mapping class group of the fibre, up to a bounded factor, where the bound depends only on the genus of the fibre.
title The triangulation complexity of fibred 3-manifolds
topic Geometric Topology
57Q15, 57N10, 57M50, 57M27
url https://arxiv.org/abs/1910.10914