Open Access
2008 Commensurators of Cusped Hyperbolic Manifolds
Oliver Goodman, Damian Heard, Craig Hodgson
Experiment. Math. 17(3): 283-306 (2008).


This paper describes a general algorithm for finding the commensurator of a nonarithmetic hyperbolic manifold with cusps and for deciding when two such manifolds are commensurable. The method is based on some elementary observations regarding horosphere packings and canonical cell decompositions. For example, we use this to find the commensurators of all nonarithmetic hyperbolic once-punctured torus bundles over the circle.

For hyperbolic 3-manifolds, the algorithm has been implemented using Goodman’s computer program Snap. We use this to determine the commensurability classes of all cusped hyperbolic 3-manifolds triangulated using at most seven ideal tetrahedra, and for the complements of hyperbolic knots and links with up to twelve crossings.


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Oliver Goodman. Damian Heard. Craig Hodgson. "Commensurators of Cusped Hyperbolic Manifolds." Experiment. Math. 17 (3) 283 - 306, 2008.


Published: 2008
First available in Project Euclid: 19 November 2008

zbMATH: 1338.57016
MathSciNet: MR2455701

Primary: 57M50
Secondary: 57M25 , 57N10

Keywords: canonical cell decomposition , commensurator , hyperbolic 3-manifolds , hyperbolic links , hyperbolic manifolds

Rights: Copyright © 2008 A K Peters, Ltd.

Vol.17 • No. 3 • 2008
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