Bounds on Pachner moves and systoles of cusped 3–manifolds

Kalelkar, Tejas; Raghunath, Sriram

doi:10.2140/agt.2022.22.2951

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Bounds on Pachner moves and systoles of cusped $3$–manifolds

Tejas Kalelkar and Sriram Raghunath

Algebraic & Geometric Topology 22 (2022) 2951–2996

DOI: 10.2140/agt.2022.22.2951

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

References

Publication

Received: 7 February 2021

Revised: 27 July 2021

Accepted: 15 August 2021

Published: 13 December 2022

Authors

Tejas Kalelkar
Mathematics Department Indian Institute of Science Education and Research Pune Pune India

Sriram Raghunath
Mathematics Department Indian Institute of Science Education and Research Pune Pune India

Volume 22, issue 6 (2022)