Lower order solvability of links

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dc.contributor.advisorHarvey, Shellyen_US
dc.contributor.committeeMemberCochran, Tim D.en_US
dc.contributor.committeeMemberGoldman, Ronen_US
dc.creatorMartin, Tayloren_US
dc.date.accessioned2013-09-16T15:55:32Zen_US
dc.date.accessioned2013-09-16T15:55:34Zen_US
dc.date.available2013-09-16T15:55:32Zen_US
dc.date.available2013-09-16T15:55:34Zen_US
dc.date.created2013-05en_US
dc.date.issued2013-09-16en_US
dc.date.submittedMay 2013en_US
dc.date.updated2013-09-16T15:55:34Zen_US
dc.description.abstractThe n-solvable filtration of the link concordance group, defined by Cochran, Orr, and Teichner in 2003, is a tool for studying smooth knot and link concordance that yields important results in low-dimensional topology. We focus on the first two stages of the n-solvable filtration, which are the class of 0-solvable links and the class of 0.5-solvable links. We introduce a new equivalence relation on links called 0-solve equivalence and establish both an algebraic and a geometric characterization 0-solve equivalent links. As a result, we completely characterize 0-solvable links and we give a classification of links up to 0-solve equivalence. We relate 0-solvable links to known results about links bounding gropes and Whitney towers in the 4-ball. We then establish a sufficient condition for a link to be 0.5-solvable and show that 0.5-solvable links must have vanishing Sato-Levine invariants.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationMartin, Taylor. "Lower order solvability of links." (2013) Diss., Rice University. <a href="https://hdl.handle.net/1911/71998">https://hdl.handle.net/1911/71998</a>.en_US
dc.identifier.slug123456789/ETD-2013-05-554en_US
dc.identifier.urihttps://hdl.handle.net/1911/71998en_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.subjectKnot theoryen_US
dc.subjectLink concordanceen_US
dc.subjectN-solvable filtrationen_US
dc.subjectBand-pass equivalenceen_US
dc.subjectMilnor's invariantsen_US
dc.titleLower order solvability of linksen_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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