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 $m\geq 3$, $p\geq 2$, $q\geq 2$.
Citation
Hugh M. Hilden. María Teresa Lozano. José María Montesinos-Amilibia. "On universal hyperbolic orbifold structures in $S^{3}$ with the Borromean rings as singularity." Hiroshima Math. J. 40 (3) 357 - 370, November 2010. https://doi.org/10.32917/hmj/1291818850
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