## Hiroshima Mathematical Journal

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

#### Abstract

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 $m\geq 3$, $p\geq 2$, $q\geq 2$.

#### Article information

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

Dates
First available in Project Euclid: 8 December 2010

https://projecteuclid.org/euclid.hmj/1291818850

Digital Object Identifier
doi:10.32917/hmj/1291818850

Mathematical Reviews number (MathSciNet)
MR2766667

Zentralblatt MATH identifier
1227.57006

#### Citation

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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