Further Study of Kanenobu Knots

Abstract

We determine the rational Khovanov bigraded homology groups of all Kanenobu knots. Also, we determine the crossing number for all Kanenobu knots $K(p,q)$ with $pq>0$ or $|pq|\le \max \{|p|,|q|\}$. In the case where $pq<0$ and $|pq|>\max \{|p|,|q|\}$, we conjecture that the crossing number is $|p|+|q|+8$.

arXiv comment16 pages, 8 figures