The algebraic crossing number and the braid index of knots and links

Details The algebraic crossing number and the braid index of knots and links The algebraic crossing number and the braid index of knots and links

2009-07-06

arxiv.org/abs/0907.1019v1

Algebr. Geom. Topol. 6 (2006) 2313-2350

Mathematics

Geometric Topology

This is the version published by Algebraic & Geometric Topology on 8 December 2006

Scientific paper

10.2140/agt.2006.6.2313

It has been conjectured that the algebraic crossing number of a link is uniquely determined in minimal braid representation. This conjecture is true for many classes of knots and links. The Morton-Franks-Williams inequality gives a lower bound for braid index. And sharpness of the inequality on a knot type implies the truth of the conjecture for the knot type. We prove that there are infinitely many examples of knots and links for which the inequality is not sharp but the conjecture is still true. We also show that if the conjecture is true for K and L, then it is also true for the (p,q)-cable of K and for the connect sum of K and L.

Affiliated with

Also associated with

No associations

Rating

The algebraic crossing number and the braid index of knots and links 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 The algebraic crossing number and the braid index of knots and links, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The algebraic crossing number and the braid index of knots and links will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-28034