The dual knots of doubly primitive knots
Saito, Toshio
Osaka J. Math., Tome 45 (2008) no. 1, p. 403-421 / Harvested from Project Euclid
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For certain $(1,1)$-knots in lens spaces with a longitudinal surgery yielding the 3-sphere, we determine a non-negative integer derived from its $(1,1)$-splitting. The value will be an invariant for such knots. Roughly, it corresponds to a `minimal' self-intersection number when one consider projections of a knot on a Heegaard torus. As an application, we give a necessary and sufficient condition for such knots to be hyperbolic.
Publié le : 2008-06-15
Classification:  57N10,  57M25 
@article{1216151106,
     author = {Saito, Toshio},
     title = {The dual knots of doubly primitive knots},
     journal = {Osaka J. Math.},
     volume = {45},
     number = {1},
     year = {2008},
     pages = { 403-421},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1216151106}
}

Saito, Toshio. The dual knots of doubly primitive knots. Osaka J. Math., Tome 45 (2008) no. 1, pp.  403-421. http://gdmltest.u-ga.fr/item/1216151106/