2 papers
math.GT2009
Companions of the unknot and width additivity
Ryan Blair, Maggy Tomova
It has been conjectured that for knots and in , $w(K#K')= w(K)+w(K')-2$. Scharlemann and Thompson have proposed potential counterexamples to this conjecture. For ever…
math.GT2006
Alternating Augmentations of Links
Ryan Blair
We show that one can interweave an unknot into any non-alternating connected projection of a link so that the resulting augmented projection is alternating.