Mathematics Colloquia and Seminars

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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.