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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
Uniqueness of bridge surfaces for 2-bridge knots
Martin Scharlemann, Maggy Tomova
Any 2-bridge knot in the 3-sphere has a bridge sphere from which any other bridge surface can be obtained by stabilization, meridional stabilization, perturbation and proper isotop…
math.GT2006
Conway products and links with multiple bridge surfaces
Martin Scharlemann, Maggy Tomova
Suppose a link K in a 3-manifold M is in bridge position with respect to two different bridge surfaces P and Q, both of which are c-weakly incompressible in the complement of K. Th…