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On the Borromean orbifolds: geometry and arithmetic Hilden, Hugh Michael Lozano Imízcoz, María Teresa Montesinos Amilibia, José María Apanasov, Boris Neumann, Walter D. Reid, Alan W. Siebenmann, Laurent 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 Papers 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. DGICYT Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T21:07:29Z 2023-06-20T21:07:29Z 1992 book part https://hdl.handle.net/20.500.14352/60745 XXXX-XXXX eng Ohio State University Mathematical Research Institute Publications PB85-0336 PB89-0105 open access application/pdf Walter de Gruyter & Co