On football manifolds of E. Molnár
\textit{E. Molnár} [Differential geometry and its applications, Proc. Conf., Dubrovnik/Yugosl. 1988, 217--241 (1989; Zbl 0694.57007)] studied compact orientable hyperbolic 3-manifolds obtained by face identification of certain solids. They are known as hyperbolic football manifolds \(M = \mathbb H^3 /G\), \(M' =\mathbb H^3 /G'\); the isometry groups \(G\) and \(G'\) are given explicitly by finite presentations. The authors show that these presentations are induced by genus 2 Heegard diagrams of \(M\) and \(M'\), that is, they are geometric. Furthermore, it is shown that \(M\) and \(M'\) are ``hyperelliptic'' which means that they permit an involution with quotient space \(S^3\). Moreover, \(M\) and \(M'\) are 2-fold coverings of \(S^3\) branched along certain 3-bridge links which are determined. Further, hyperbolic 3-manifolds are proved to be hyperelliptic.
scientific article; zbMATH DE number 5848543