Link Concordance and Groups

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dc.contributor.advisorHarvey, Shelly Len_US
dc.creatorKuzbary, Miriamen_US
dc.date.accessioned2019-05-17T18:49:56Zen_US
dc.date.available2019-05-17T18:49:56Zen_US
dc.date.created2019-05en_US
dc.date.issued2019-04-12en_US
dc.date.submittedMay 2019en_US
dc.date.updated2019-05-17T18:49:56Zen_US
dc.description.abstractThis work concerns the study of link concordance using groups, both extracting concordance data from group theoretic invariants and determining the properties of group structures on links modulo concordance. Milnor's invariants are one of the more fundamental link concordance invariants; they are thought of as higher order linking numbers and can be computed using both Massey products (due to Turaev and Porter) and higher order intersections (due to Cochran). In this thesis, we generalize Milnor's invariants to knots inside a closed, oriented 3-manifold M. We call this the Dwyer number of a knot and show methods to compute it for null-homologous knots inside a family of 3-manifolds with free fundamental group. We further show the Dwyer number provides the weight of the first non-vanishing Massey product in the knot complement in the ambient manifold. Additionally, we prove the Dwyer number detects knots K in M bounding smoothly embedded disks in specific 4-manifolds with boundary M which are not concordant to the unknot. This result further motivates our definition of a new link concordance group using the knotification construction of Ozsvath and Szabo. Finally, we give a proof that the string link concordance group modulo its pure braid subgroup is non-abelian.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationKuzbary, Miriam. "Link Concordance and Groups." (2019) Diss., Rice University. <a href="https://hdl.handle.net/1911/105956">https://hdl.handle.net/1911/105956</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/105956en_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.subjectlow dimensional topologyen_US
dc.subjectgeometric topologyen_US
dc.subjectlink concordanceen_US
dc.subjectknot concordanceen_US
dc.subjectgroup theoryen_US
dc.subjectnilpotent groupsen_US
dc.subjectMilnor's invariantsen_US
dc.subjectHeegaard Floer homologyen_US
dc.titleLink Concordance and Groupsen_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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