Two-fold branched covers

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Show simple item record Auckly, David R. 2014-08-04T14:29:40Z 2014-08-04T14:29:40Z 2014-08-04
dc.description.abstract Many three-dimensional manifolds are two-fold branched covers of the three-dimensional sphere. However, there are some that are not. This paper includes exposition about two-fold branched covers and includes many examples. It shows that there are three-dimensional homology spheres that do not two-fold branched cover any manifold, ones that only two-fold branched cover the three-dimensional sphere, ones that just two-fold branched cover a non-trivial manifold, and ones that two-fold branched cover both the sphere and non-trivial manifolds. When a manifold is surgery on a knot, the possible quotients via involutions generically correspond to quotients of the knot. There can, however, be a finite number of surgeries for which there are exceptional additional symmetries. The included proof of this result follows the proof of Thurston's Dehn surgery theorem. The paper also includes examples of such exceptional symmetries. Since the quotients follow the behavior of knots, a census of the behavior for knots with less than 11 crossings is included. en_US
dc.language.iso en_US en_US
dc.relation.uri en_US
dc.rights Electronic version of an article published as Journal of Knot Theory and Its Ramifications, 23(3), 1430001. DOI: 10.1142/S0218216514300018 © copyright World Scientific Publishing Company en_US
dc.subject Branched covers en_US
dc.subject Hyperbolic geometry en_US
dc.subject Dehn Surgery en_US
dc.subject Symmetries en_US
dc.subject Exceptional Surgeries en_US
dc.title Two-fold branched covers en_US
dc.type Article (author version) en_US 2014 en_US
dc.citation.doi doi:10.1142/S0218216514300018 en_US
dc.citation.issue 3 en_US
dc.citation.jtitle Journal of Knot Theory and Its Ramifications en_US
dc.citation.spage 1430001 en_US
dc.citation.volume 23 en_US
dc.contributor.authoreid dav en_US

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