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## February 2019

### A nonorientable version of the Milnor Conjecture (Cornelia A. Van Cott, USF)

In 1968, Milnor famously conjectured that the smooth 4-genus of the torus knot T(p,q) is given by (p-1)(q-1)/2. This conjecture was first verified by Kronheimer and Mrowka in 1993 and has received several other proofs since then. In this talk, we discuss a nonorientable analogue of this conjecture, first formulated by Josh Batson. We prove the conjecture for infinite families of of torus knots, using tools from knot Floer homology. We also connect the problem to the world of continued…

Find out more »## March 2019

### Non-existence of epimorphisms between certain genus two handlebody-knot groups (Ryo Nikkuni, Tokyo Woman’s Christian University)

For two genus $g$ handlebody-knots $H_{1}$ and $H_{2}$, we denote $H_{1} \geq H_{2}$ if there exists an epimorphism from the fundamental group of the handlebody-knot complement of $H_{1}$ onto the one of $H_{2}$. In the case of $g = 1$, this order is a partial order on the set of prime knots and has been determined up to $11$ crossings by Kitano-Suzuki and Horie-Kitano-Matsumoto-Suzuki. In this talk, we consider the case of $g = 2$ and exhibit a lot of…

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