Alternating genera of torus knots
The alternating genus of a knot is the minimum genus of a surface onto which the knot has an alternating diagram satisfying certain conditions. Very little is currently known about this knot invariant. We study spanning surfaces for knots, and define a new alternating distance which can be calculated exactly for all torus knots. This gives a lower bound on the alternating genus, and allows us to classify all toroidally alternating torus knots.
Dr Josh Howie, Monash University