Hilden, Hugh MichaelLozano Imízcoz, María TeresaMontesinos Amilibia, José MaríaApanasov, BorisNeumann, Walter D.Reid, Alan W.Siebenmann, Laurent2023-06-202023-06-2019923-11-012598-6https://hdl.handle.net/20.500.14352/60745Papers from the Research Semester in Low-dimensional Topology held at Ohio State University, Columbus, Ohio, February–June 1990.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.engbook partopen access515.14Borromean orbifoldsarithmeticitysingular setBorromean ringsarithmetic hyperbolic orbifoldhyperbolic structures of the Borromean orbifoldsGeometria algebraicaTopología1201.01 Geometría Algebraica1210 Topología