Translator Disclaimer
November 2010 On universal hyperbolic orbifold structures in $S^{3}$ with the Borromean rings as singularity
Hugh M. Hilden, María Teresa Lozano, José María Montesinos-Amilibia
Hiroshima Math. J. 40(3): 357-370 (November 2010). DOI: 10.32917/hmj/1291818850

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

Download 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

Information

Published: November 2010
First available in Project Euclid: 8 December 2010

zbMATH: 1227.57006
MathSciNet: MR2766667
Digital Object Identifier: 10.32917/hmj/1291818850

Subjects:
Primary: 57M12, 57M25, 57M50

Rights: Copyright © 2010 Hiroshima University, Mathematics Program

JOURNAL ARTICLE
14 PAGES


SHARE
Vol.40 • No. 3 • November 2010
Back to Top