Abstract
Two of the main methods for the construction of closed orientable 3-manifolds, and in particular of hyperbolic 3-manifolds, are surgery on links and branched coverings of links. If the link is hyperbolic, i.e., has hyperbolic complement, by results of Thurston most of the resulting 3-manifolds are hyperbolic. In the present paper, for a fixed integer n ⩾ 2, we consider hyperbolic 3-manifolds M n, k which are cyclic n-fold branched coverings of a hyperbolic link with two components. Our main theorem relates the classification up to isometry or homeomorphism of these manifolds to the symmetry group of the link and allows a complete classification of these manifolds in various cases; as an example, we consider cyclic branched coverings of the Whitehead link. The classification resembles the classification of lens spaces which are the cyclic branched coverings of the Hopf link (which is not hyperbolic, however); it generalizes to links with more than two components. For the proof, which consists in a mixture of geometric and algebraic arguments, we extend methods used in [5] in a special case.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.