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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.
Keywords
Hauptvermutung, ideal triangulations, hyperbolic knots,
Pachner moves, systole length
Mathematical Subject Classification
Primary: 57K10, 57K32, 57Q25
Publication
Received: 7 February 2021
Revised: 27 July 2021
Accepted: 15 August 2021
Published: 13 December 2022