On finite index subgroups of a universal group

Details On finite index subgroups of a universal group On finite index subgroups of a universal group

2007-10-31

arxiv.org/abs/0710.5835v1

Mathematics

Geometric Topology

15 pages, 9 figures

Scientific paper

The orbifold group of the Borromean rings with singular angle 90 degrees, $U$, is a universal group, because every closed oriented 3--manifold $M^{3}$ occurs as a quotient space $M^{3} = H^{3}/G$, where $G$ is a finite index subgroup of $U$. Therefore, an interesting, but quite difficult problem, is to classify the finite index subgroups of the universal group $U$. One of the purposes of this paper is to begin this classification. In particular we analyze the classification of the finite index subgroups of $U$ that are generated by rotations.

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