descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jan 2008Embargo end date: 01 Jan 2008 English Publisher:Informa UK LimitedJournal:Experimental Mathematics, volume 17, pages 283-306 (issn: 1058-6458, eissn: 1944-950X,

Authors: Goodman, O; Heard, D; Hodgson, C;

doi: 10.1080/10586458.2008.10129044 , 10.48550/arxiv.0801.4815

arXiv: http://arxiv.org/abs/0801.4815

handle: 11343/29220

Commensurators of Cusped Hyperbolic Manifolds

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Abstract

This paper describes a general algorithm for finding the commensurator of a non-arithmetic cusped hyperbolic manifold, 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 non-arithmetic 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 7 ideal tetrahedra, and for the complements of hyperbolic knots and links with up to 12 crossings.

32 pages, 46 figures; to appear in "Experimental Mathematics"

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University of Melbourne
Australia

Keywords

hyperbolic 3-manifolds, hyperbolic links, Geometric Topology (math.GT), Pure Mathematics, 57M50, 57N10, Mathematics - Geometric Topology, 57M25, commensurator, canonical cell decomposition, FOS: Mathematics, 57M50, 57M27, Hyperbolic manifolds

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Snap for hyperbolic 3-manifolds software on SourceForge
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