Bounds on Pachner moves and systoles of cusped 3-manifolds

Tejas Kalelkar; Sriram Raghunath

doi:10.2140/agt.2022.22.2951

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arXiv · 2007.02781

Bounds on Pachner moves and systoles of cusped 3-manifolds

Tejas Kalelkar·Sriram Raghunath

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Abstract

Any two geometric ideal triangulations of a cusped complete hyperbolic $3$-manifold $M$ 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 $M$, we also give a lower bound on the systole length of $M$ in terms of the number of tetrahedra and a lower bound on dihedral angles.

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Tejas Kalelkar, Sriram Raghunath. 2020-07-06. Bounds on Pachner moves and systoles of cusped 3-manifolds. https://doi.org/10.2140/agt.2022.22.2951

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