Title : Doubly composite knots with unknotting number $1$
Speaker : Cameron Gordon (University of Texas at Austin)
Abstract :

We will describe joint work with John Luecke on the question of when a knot with non-empty characteristic toric 2-suborbifold splitting in the sense of Bonahon-Siebenmann can have unknotting number 1. Consequences include the facts that there is a (practical) algorithm to decide whether or not a given Conway-algebraic knot has unknotting number 1, and that having unknotting number 1 is invariant under mutation.

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