On universal hyperbolic orbifold structures in $S^{3}$ with the Borromean rings as singularity
Hilden, Hugh M. ; Lozano, María Teresa ; Montesinos-Amilibia, José María
Hiroshima Math. J., Tome 40 (2010) no. 1, p. 357-370 / Harvested from Project Euclid
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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 $m\geq 3$, $p\geq 2$, $q\geq 2$.
Publié le : 2010-11-15
Classification:  Orbifold,  Borromean rings,  universal orbifold,  57M25,  57M12,  57M50 
@article{1291818850,
     author = {Hilden, Hugh M. and Lozano, Mar\'\i a Teresa and Montesinos-Amilibia, Jos\'e Mar\'\i a},
     title = {On universal hyperbolic orbifold structures in $S^{3}$ with the Borromean rings as singularity},
     journal = {Hiroshima Math. J.},
     volume = {40},
     number = {1},
     year = {2010},
     pages = { 357-370},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1291818850}
}

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., Tome 40 (2010) no. 1, pp.  357-370. http://gdmltest.u-ga.fr/item/1291818850/