A closed 3-manifold M is said to be hyperelliptic if it has an involution \tau such that the quotient space of M by the action of \tau is homeomorphic to the standard 3-sphere. We show that the hyperbolic football manifolds of Emil Molnár (1988) are hyperelliptic. Then we determine the isometry groups of suchmanifolds. Another consequence is that the unique hyperbolic dodecahedral and icosahedral 3-space forms with first homology group Z_35 (constructed by I. Prok in 1998, on the basis of a principal algorithm due to Emil Molnár, and byRichardson and Rubinstein in 1982) are also hyperelliptic.
ON FOOTBALL MANIFOLDS OF E. MOLNAR / Cavicchioli, Alberto; Telloni, Agnese Ilaria. - In: ACTA MATHEMATICA HUNGARICA. - ISSN 0236-5294. - STAMPA. - 124:(2009), pp. 321-332. [10.1007/s10474-009-8196-9]
ON FOOTBALL MANIFOLDS OF E. MOLNAR
CAVICCHIOLI, Alberto;TELLONI, Agnese Ilaria
2009
Abstract
A closed 3-manifold M is said to be hyperelliptic if it has an involution \tau such that the quotient space of M by the action of \tau is homeomorphic to the standard 3-sphere. We show that the hyperbolic football manifolds of Emil Molnár (1988) are hyperelliptic. Then we determine the isometry groups of suchmanifolds. Another consequence is that the unique hyperbolic dodecahedral and icosahedral 3-space forms with first homology group Z_35 (constructed by I. Prok in 1998, on the basis of a principal algorithm due to Emil Molnár, and byRichardson and Rubinstein in 1982) are also hyperelliptic.
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