Browsing by Author "Williams, Shawn"

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    Extensions of the Fox-Milnor Condition
    (2022-04-22) Williams, Shawn; Harvey, Shelly
    The search for slice knots is an important task in low dimensional topology. In the 1960s, Fox and Milnor proved a theorem stating that the Alexander polynomial of a slice knot satisfies a special factorization. A decade later, Kawauchi extended this theorem for the multivariable Alexander polynomial of slice links. This factorization, known as the Fox-Milnor condition, has been used and generalized many times as an obstruction to a link being slice. In this defense, we will see two more extensions of this condition, first to the multivariable Alexander polynomial of 1-solvable links, and then for the first order Alexander polynomial of ribbon knots.