Jointly primitive knots and surgeries between lens spaces
Date
2019-04-05Author
Baker, Kenneth L.
Hoffman, Neil R.
Licata, Joan E.
Metadata
Show full item recordAbstract
This paper describes a Dehn surgery approach to generating asymmetric hyperbolic manifolds with two distinct lens space fillings. Such manifolds were first identified
in work of Dunfield-Hoffman-Licata as the result of a computer search of the SnapPy census, but the current work establishes a topological framework for constructing vastly many more such examples. We introduce the notion of a ``jointly primitive'' presentation of a knot and show that a refined version of this condition ``longitudinally jointly primitive'' is equivalent to being surgery dual to a (1,2)--knot in a lens space. This generalizes Berge's equivalence between having a doubly primitive presentation and being surgery dual to a (1,1)--knot in a lens space. Through surgery descriptions on a seven-component link in S3, we provide several explicit multi-parameter infinite families of knots in lens spaces with longitudinal jointly primitive presentations and observe among them all the examples previously seen in Dunfield-Hoffman-Licata.
Citation
Baker, K.L., Hoffman, N.R., Licata, J.E. (2019). Jointly primitive knots and surgeries between lens spaces.