The canonical genus for Whitehead doubles of a family of alternating knots

Hee Jeong Jang, Sang Youl Lee

For any given integer $r\ge 1$ and a quasitoric braid ${\beta }_r=({\sigma }_r^{-\epsilon }{\sigma }_{r-1}^{\epsilon }...$ ${\sigma }_1^{(-1{)}^r\epsilon }{)}^3$ with $\epsilon =\pm 1$, we prove that the maximum degree in $z$ of the HOMFLYPT…