On universal hyperbolic orbifold structures in \(S^3\) with the Borromean rings as singularity
Denote by \(B\) the Borromean rings. Let \(a\), \(b\) and \(c\) be the components of \(B\). The main result of the paper is Theorem~1. Given integers \(r\geq 3\), \(p\geq 2\), \(q\geq 2\), every \(3\)-manifold \(M^3\) is a covering \(M^3 \to S^3\) over \(B\) such that the branching indices upon \(a\) are \(\{1,2,2p\}\), upon \(b\) are \(\{1,2,2q\}\), and upon \(c\) are all \(r\). As a corollary, we have that the hyperbolic orbifold \(\mathbf{B}_{r,2p,2q}\), \(r\geq 3\), \(p\geq 2\), \(q\geq 2\), is universal.
scientific article; zbMATH DE number 5872136
scientific article