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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)
Abstract: 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.
Description: 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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