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Title: On quotient orbifolds of hyperbolic 3-manifolds of genus two
Authors: Bruno, Annalisa
Mecchia, Mattia
Keywords: Genus two3-manifold3-bridge knot2-fold branched coveringquotient orbifold
Issue Date: 23-Dec-2014
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
46 (2014)
We analyse the orbifolds that can be obtained as quotients of genus two hyperbolic 3-manifolds by their orientation preserving isometry groups. The genus two hyperbolic 3-manifolds are exactly the hyperbolic2-fold branched coverings of 3-bridge links. If the3-bridge link is a knot, we prove that the underlying topological space of the quotient orbifold is either the 3-sphere or a lens space and we describe the combinatorial setting of the singular set for each possible isometry group. In the case of 3-bridge links with two or three components, the situation is more complicated and we show that the underlying topological space is the3-sphere, a lens space or a prism manifold. Finally we present an infnite family of hyperbolic 3-manifolds that are simultaneously the 2-foldbranched covering of three inequivalent knots, two with bridge number three and the third one with bridge number strictly greater than three.
Annalisa Bruno and Mattia Mecchia, "On quotient orbifolds of hyperbolic -manifolds of genus two", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 46 (2014), pp.271-299
ISSN: 0049-4704
Appears in Collections:Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics vol.46 (2014)

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