Extensions of the Fox-Milnor Condition

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dc.contributor.advisorHarvey, Shellyen_US
dc.creatorWilliams, Shawnen_US
dc.date.accessioned2022-09-26T15:16:49Zen_US
dc.date.available2022-09-26T15:16:49Zen_US
dc.date.created2022-05en_US
dc.date.issued2022-04-22en_US
dc.date.submittedMay 2022en_US
dc.date.updated2022-09-26T15:16:49Zen_US
dc.description.abstractThe 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.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationWilliams, Shawn. "Extensions of the Fox-Milnor Condition." (2022) Diss., Rice University. <a href="https://hdl.handle.net/1911/113356">https://hdl.handle.net/1911/113356</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/113356en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectknotsen_US
dc.subjectlinksen_US
dc.subjectsliceen_US
dc.subjectsolvabilityen_US
dc.subjectFox-Milnoren_US
dc.subjectfactorizationen_US
dc.subjectlocalizationen_US
dc.subjectAlexander moduleen_US
dc.subjectAlexander polynomialen_US
dc.titleExtensions of the Fox-Milnor Conditionen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematicsen_US
thesis.degree.disciplineNatural Sciencesen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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