On the Braid Index of Kanenobu Knots
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We study the braid indices of the Kanenobu knots. It is known that the Kanenobuknots have the same HOMFLYPT polynomial and the same Khovanov-Rozanskyhomology. The MFW inequality is known for giving a lower bound of the braid index of alink by applying the HOMFLYPT polynomial. Therefore, it is not easy to determine thebraid indices of the Kanenobu knots. In our previous paper, we gave upper bounds andsharper lower bounds of the braid indices of the Kanenobu knots by applying the 2-cableversion of the zeroth coefficient HOMFLYPT polynomial. In this paper, we give sharperupper bounds of the braid indices of the Kanenobu knots.
Abstract
We study the braid indices of the Kanenobu knots. It is known that the Kanenobuknots have the same HOMFLYPT polynomial and the same Khovanov-Rozanskyhomology. The MFW inequality is known for giving a lower bound of the braid index of alink by applying the HOMFLYPT polynomial. Therefore, it is not easy to determine thebraid indices of the Kanenobu knots. In our previous paper, we gave upper bounds andsharper lower bounds of the braid indices of the Kanenobu knots by applying the 2-cableversion of the zeroth coefficient HOMFLYPT polynomial. In this paper, we give sharperupper bounds of the braid indices of the Kanenobu knots.
참고문헌 (12)
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