On the Borromean orbifolds: geometry and arithmetic



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Hilden, Hugh Michael and Lozano Imízcoz, María Teresa and Montesinos Amilibia, José María (1992) On the Borromean orbifolds: geometry and arithmetic. In Topology '90. Ohio State University Mathematical Research Institute Publications (1). Walter de Gruyter & Co, Berlin, pp. 133-167. ISBN 3-11-012598-6

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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.

Item Type:Book Section
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Papers from the Research Semester in Low-dimensional Topology held at Ohio State University, Columbus, Ohio, February–June 1990.

Uncontrolled Keywords:Borromean orbifolds; arithmeticity; singular set; Borromean rings; arithmetic hyperbolic orbifold; hyperbolic structures of the Borromean orbifolds
Subjects:Sciences > Mathematics > Algebraic geometry
Sciences > Mathematics > Topology
ID Code:22138
Deposited On:27 Jun 2013 16:59
Last Modified:09 Sep 2020 08:17

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