The (n)-Solvable Filtration of the Link Concordance Group and Milnor's mu-Invariaants

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dc.contributor.advisorHarvey, Shellyen_US
dc.creatorOtto, Carolyn Annen_US
dc.date.accessioned2013-03-08T00:37:23Zen_US
dc.date.available2013-03-08T00:37:23Zen_US
dc.date.issued2011en_US
dc.description.abstractWe establish several new results about the ( n )-solvable filtration, [Special characters omitted.] , of the string link concordance group [Special characters omitted.] . We first establish a relationship between ( n )-solvability of a link and its Milnor's μ-invariants. We study the effects of the Bing doubling operator on ( n )-solvability. Using this results, we show that the "other half" of the filtration, namely [Special characters omitted.] , is nontrivial and contains an infinite cyclic subgroup for links with sufficiently many components. We will also show that links modulo (1)-solvability is a nonabelian group. Lastly, we prove that the Grope filtration, [Special characters omitted.] of [Special characters omitted.] is not the same as the ( n )-solvable filtration.en_US
dc.format.extent69 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH. 2011 OTTOen_US
dc.identifier.citationOtto, Carolyn Ann. "The (n)-Solvable Filtration of the Link Concordance Group and Milnor's mu-Invariaants." (2011) Diss., Rice University. <a href="https://hdl.handle.net/1911/70379">https://hdl.handle.net/1911/70379</a>.en_US
dc.identifier.digitalOttoCen_US
dc.identifier.urihttps://hdl.handle.net/1911/70379en_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.subjectPure sciencesen_US
dc.subjectKnot theoryen_US
dc.subjectLink concordanceen_US
dc.subjectSolvable filtrationen_US
dc.subjectString linksen_US
dc.subjectMathematicsen_US
dc.titleThe (n)-Solvable Filtration of the Link Concordance Group and Milnor's mu-Invariaantsen_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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