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Bounds on Pachner moves
and systoles of cusped $3$–manifolds
Tejas Kalelkar and Sriram Raghunath |
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Algebraic & Geometric Topology 22 (2022) 2951–2996
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DOI: 10.2140/agt.2022.22.2951
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Abstract |
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Any two geometric ideal triangulations of a cusped complete hyperbolic –manifold are related by a sequence of Pachner moves through topological triangulations. We give a bound on the length of this sequence in terms of the total number of tetrahedra and a lower bound on dihedral angles. This leads to a naive but effective algorithm to check if two hyperbolic knots are equivalent, given geometric ideal triangulations of their complements. Given a geometric ideal triangulation of , we also give a lower bound on the systole length of in terms of the number of tetrahedra and a lower bound on dihedral angles. |
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Keywords
Hauptvermutung, ideal triangulations, hyperbolic knots,
Pachner moves, systole length
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Mathematical Subject Classification
Primary: 57K10, 57K32, 57Q25
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References |
Publication
Received: 7 February 2021
Revised: 27 July 2021
Accepted: 15 August 2021
Published: 13 December 2022
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Authors |
| Tejas Kalelkar | |
| Mathematics Department Indian Institute of Science Education and Research Pune Pune India |
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| Sriram Raghunath | |
| Mathematics Department Indian Institute of Science Education and Research Pune Pune India |
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