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The
triangulation complexity of fibred $3$–manifolds
Marc Lackenby and Jessica S Purcell |
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Geometry & Topology 28 (2024) 1727–1828
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Abstract |
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The triangulation complexity of a closed orientable –manifold is the minimal number of tetrahedra in any triangulation of . Our main theorem gives upper and lower bounds on the triangulation complexity of any closed orientable hyperbolic –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 . |
Keywords
triangulation complexity, $3$–manifold, fibred,
pseudo-Anosov
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Mathematical Subject Classification
Primary: 57K20, 57K30, 57Q15
Secondary: 57K32
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References |
Publication
Received: 6 April 2021
Revised: 21 July 2022
Accepted: 30 September 2022
Published: 18 July 2024
Proposed: Ian Agol
Seconded: Mladen Bestvina, David Fisher
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Authors |
| Marc Lackenby | |
| Mathematical Institute University of Oxford Oxford United Kingdom |
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| Jessica S Purcell | |
| School of Mathematics Monash University Melbourne VIC Australia |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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