Extensions of the Fox-Milnor Condition

Date
2022-04-22
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Abstract

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.

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Degree
Doctor of Philosophy
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Thesis
Keywords
knots, links, slice, solvability, Fox-Milnor, factorization, localization, Alexander module, Alexander polynomial
Citation

Williams, Shawn. "Extensions of the Fox-Milnor Condition." (2022) Diss., Rice University. https://hdl.handle.net/1911/113356.

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