On quotient orbifolds of hyperbolic 3-manifolds of genus two

Annalisa Bruno; Mattia Mecchia

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arXiv · 1411.0914

On quotient orbifolds of hyperbolic 3-manifolds of genus two

Annalisa Bruno·Mattia Mecchia

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Abstract

We analyze the orbifolds that can be obtained as quotients of hyperbolic 3-manifolds admitting a Heegaard splitting of genus two by their orientation preserving isometry groups. The genus two hyperbolic 3-manifolds are exactly the hyperbolic 2-fold branched coverings of 3-bridge links. If the 3-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 the 3-sphere, a lens space or a prism manifold. Finally we present a infinite family of hyperbolic 3-manifolds that are simultaneously the 2-fold branched covering of two inequivalent knot, one with bridge number three and the other one with bridge number strictly greater than three.

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BibTeX RIS

Annalisa Bruno, Mattia Mecchia. 2014-11-04. On quotient orbifolds of hyperbolic 3-manifolds of genus two. https://arxiv.org/abs/1411.0914

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