On the Borromean orbifolds: geometry and arithmetic
This paper continues earlier work by the authors [see, in particular, H. M. Hilden et al., Invent. Math. 87 (1987), no. 3, 441–456; H. M. Hilden, M. T. Lozano and J. M. Montesinos, in Differential topology (Siegen, 1987), 1–13, Lecture Notes in Math., 1350, Springer, Berlin, 1988;] on universal knot...
| Authors: | , , |
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| Format: | book part |
| Publication Date: | 1992 |
| Country: | España |
| Institution: | Universidad Complutense de Madrid (UCM) |
| Repository: | Docta Complutense |
| Language: | English |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/60745 |
| Online Access: | https://hdl.handle.net/20.500.14352/60745 |
| Access Level: | Open access |
| Keyword: | 515.14 Borromean orbifolds arithmeticity singular set Borromean rings arithmetic hyperbolic orbifold hyperbolic structures of the Borromean orbifolds Geometria algebraica Topología 1201.01 Geometría Algebraica 1210 Topología |
| Summary: | This paper continues earlier work by the authors [see, in particular, H. M. Hilden et al., Invent. Math. 87 (1987), no. 3, 441–456; H. M. Hilden, M. T. Lozano and J. M. Montesinos, in Differential topology (Siegen, 1987), 1–13, Lecture Notes in Math., 1350, Springer, Berlin, 1988;] on universal knots, links and groups, which shows that every closed oriented 3-manifold has the structure of an arithmetic orbifold. Investigating "how rare a flower is an arithmetic orbifold in the garden of hyperbolic orbifolds", the authors produce a three-parameter family B(m,n,p), 3≤m,n,p≤∞, of them with singular set the Borromean rings and show (simultaneously providing an excellent survey on arithmetic hyperbolic groups and orbifolds) that only eleven of its members are arithmetic. |
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