Hiroshima Mathematical Journal

On universal hyperbolic orbifold structures in $S^{3}$ with the Borromean rings as singularity

Hugh M. Hilden, María Teresa Lozano, and José María Montesinos-Amilibia

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An orientable $3$-orbifold is universal iff every closed, orientable $3$-manifold is the underlying space of an orbifold structure that is an orbifold-covering of it. The first known example of universal orbifold was $\textbf{B}_{4,4,4}=(S^{3}, B,4)$ where $B$ denotes the Borromean rings and all the isotropy groups are cyclic of order 4. The main result in this article is that the hyperbolic orbifold $\textbf{B}_{m,2p,2q}$ is universal for every $m\geq 3$, $p\geq 2$, $q\geq 2$.

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Hiroshima Math. J., Volume 40, Number 3 (2010), 357-370.

First available in Project Euclid: 8 December 2010

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Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M12: Special coverings, e.g. branched 57M50: Geometric structures on low-dimensional manifolds

Orbifold Borromean rings universal orbifold


Hilden, Hugh M.; Lozano, María Teresa; Montesinos-Amilibia, José María. On universal hyperbolic orbifold structures in $S^{3}$ with the Borromean rings as singularity. Hiroshima Math. J. 40 (2010), no. 3, 357--370. doi:10.32917/hmj/1291818850. https://projecteuclid.org/euclid.hmj/1291818850

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