Meridian twisting of closed braids and the Homfly polynomial

Details Meridian twisting of closed braids and the Homfly polynomial Meridian twisting of closed braids and the Homfly polynomial

2008-03-02

arxiv.org/abs/0803.0103v1

Mathematics

Geometric Topology

14 pages

Scientific paper

Let $\beta$ be a braid on $n$ strands, with exponent sum $w$. Let $\Delta$ be the Garside half-twist braid. We prove that the coefficient of $v^{w-n+1}$ in the Homfly polynomial of the closure of $\beta$ agrees with $(-1)^{n-1}$ times the coefficient of $v^{w+n^2-1}$ in the Homfly polynomial of the closure of $\beta\Delta^2$. This coincidence implies that the lower Morton--Franks-Williams estimate for the $v$--degree of the Homfly polynomial of $\hat\beta$ is sharp if and only if the upper MFW estimate is sharp for the $v$--degree of the Homfly polynomial of $\hat{\beta\Delta^2}$.

Affiliated with

Also associated with

No associations

Rating

Meridian twisting of closed braids and the Homfly polynomial does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Meridian twisting of closed braids and the Homfly polynomial, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Meridian twisting of closed braids and the Homfly polynomial will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-359647