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...

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Detalles Bibliográficos
Autores: Hilden, Hugh Michael, Lozano Imízcoz, María Teresa, Montesinos Amilibia, José María
Tipo de recurso: capítulo de libro
Fecha de publicación:1992
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/60745
Acceso en línea:https://hdl.handle.net/20.500.14352/60745
Access Level:acceso abierto
Palabra clave: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
Descripción
Sumario: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.