The triangulation complexity of fibred 3-manifolds
Geometric Topology
2024-07-24 v3
Abstract
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.
Keywords
Cite
@article{arxiv.1910.10914,
title = {The triangulation complexity of fibred 3-manifolds},
author = {Marc Lackenby and Jessica S. Purcell},
journal= {arXiv preprint arXiv:1910.10914},
year = {2024}
}
Comments
77 pages, 34 figures. v3: revised final version. Accepted by Geometry & Topology