The triangulation complexity of fibred 3-manifolds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866909264405069824 |
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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 |