Companions of the Unknot and Width Additivity

Abstract

It has been conjectured that for knots K and K′ in S3, w(K#K′) = w(K)+w(K′)−2. In [7], Scharlemann and Thompson proposed potential counterexamples to this conjecture. For every n, they proposed a family of knots {Kn i } for which they conjectured that w(Bn#Kn i ) = w(Kn i ) where Bn is a bridge number n knot. We show that for n > 2 none of the knots in {Kn… (More)

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