On the Braid Index of Kanenobu Knots

Takioka, Hideo

  • Received : 2013.11.08
  • Accepted : 2014.07.14
  • Published : 2015.03.23


We study the braid indices of the Kanenobu knots. It is known that the Kanenobu knots have the same HOMFLYPT polynomial and the same Khovanov-Rozansky homology. The MFW inequality is known for giving a lower bound of the braid index of a link by applying the HOMFLYPT polynomial. Therefore, it is not easy to determine the braid indices of the Kanenobu knots. In our previous paper, we gave upper bounds and sharper lower bounds of the braid indices of the Kanenobu knots by applying the 2-cable version of the zeroth coefficient HOMFLYPT polynomial. In this paper, we give sharper upper bounds of the braid indices of the Kanenobu knots.


braid index;HOMFLYPT polynomial;Kanenobu knot;2-cable knot


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