Twofold unbranched coverings of genus two 3-manifolds are hyperelliptic |
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Authors: | Alexander Mednykh Marco Reni |
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Institution: | (1) Novosibirsk, Sobolev Institute of Mathematics, 630090, Russia;(2) Dipartimento di Scienze Matematiche, Università degli Studi di Trieste, Piazzale Europa, 1, 34100 Trieste, Italy |
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Abstract: | A closed 3-dimensional manifold is hyperelliptic if it admits an involution such that the quotient space of the manifold by
the action of the involution is homeomorphic to the 3-sphere. We prove that a twofold unbranched covering of a genus two 3-manifold
is hyperelliptic. This result is reminiscent of a theorem, which seems to have first appeared in a paper by Enriques and which
has been reproved more recently by Farkas and Accola, which states that a twofold unbranched covering of a Riemann surface
of genus two is hyperelliptic. |
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