Commensurators of Cusped Hyperbolic Manifolds
| Autor: | Oliver Goodman, Damian Heard, Craig D. Hodgson |
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| Rok vydání: | 2008 |
| Předmět: |
Pure mathematics
Mathematics::Dynamical Systems Hyperbolic group General Mathematics hyperbolic links Relatively hyperbolic group Mathematics - Geometric Topology 57N10 Horosphere FOS: Mathematics 57M50 57M27 canonical cell decomposition Hyperbolic manifolds Mathematics::Symplectic Geometry Hyperbolic equilibrium point Mathematics Hyperbolic tree hyperbolic 3-manifolds Hyperbolic 3-manifold Mathematical analysis Hyperbolic manifold Geometric Topology (math.GT) Mathematics::Geometric Topology 57M50 57M25 commensurator Hyperbolic angle |
| Zdroj: | Experiment. Math. 17, iss. 3 (2008), 283-306 |
| ISSN: | 1944-950X 1058-6458 |
| DOI: | 10.1080/10586458.2008.10129044 |
| Popis: | 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. Comment: 32 pages, 46 figures; to appear in "Experimental Mathematics" |
| Databáze: | OpenAIRE |
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