On football manifolds of E. Molnár

A closed 3-manifold M is said to be hyperelliptic if it has an involution τ such that the quotient space of M by the action of τ is homeomorphic to the standard 3-sphere. We show that the hyperbolic football manifolds of Emil Molnár [12] are hyperelliptic. Then we determine the isometry groups of such manifolds. Another consequence is that the unique hyperbolic dodecahedral and icosahedral 3-space forms with first homology group ℤ 35 (constructed by I. Prok in [16], on the basis of a principal algorithm due to Emil Molnár [13], and by Richardson and Rubinstein in [18]) are also hyperelliptic.