2-Bridge knot boundary slopes: diameter and genus
Mattman, Thomas W. ; Maybrun, Gabriel ; Robinson, Kristin
Osaka J. Math., Tome 45 (2008) no. 1, p. 471-489 / Harvested from Project Euclid
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We prove that for $2$-bridge knots, the diameter, $D$, of the set of boundary slopes is twice the crossing number, $c$. This constitutes partial verification of a conjecture that, for all knots in $S^{3}$, $D \leq 2 c$. In addition, we characterize the $2$-bridge knots with four or fewer boundary slopes and show that they each have a boundary slope of genus two or less.
Publié le : 2008-06-15
Classification:  57M25,  57M27 
@article{1216151110,
     author = {Mattman, Thomas W. and Maybrun, Gabriel and Robinson, Kristin},
     title = {2-Bridge knot boundary slopes: diameter and genus},
     journal = {Osaka J. Math.},
     volume = {45},
     number = {1},
     year = {2008},
     pages = { 471-489},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1216151110}
}

Mattman, Thomas W.; Maybrun, Gabriel; Robinson, Kristin. 2-Bridge knot boundary slopes: diameter and genus. Osaka J. Math., Tome 45 (2008) no. 1, pp.  471-489. http://gdmltest.u-ga.fr/item/1216151110/