Higher-order linking forms

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dc.contributor.advisorCochran, Tim D.en_US
dc.creatorLeidy, Constanceen_US
dc.date.accessioned2009-06-04T06:40:55Zen_US
dc.date.available2009-06-04T06:40:55Zen_US
dc.date.issued2004en_US
dc.description.abstractTrotter [T] found examples of knots that have isomorphic classical Alexander modules, but non-isomorphic classical Blanchfield linking forms. T. Cochran [C] defined higher-order Alexander modules, An , (K), of a knot, K, and higher-order linking forms, Bℓn (K), which are linking forms defined on An , (K). When n = 0, these invariants are just the classical Alexander module and Blanchfield linking form. The question was posed in [C] whether Trotter's result generalized to the higher-order invariants. We show that it does. That is, we construct examples of knots that have isomorphic nth-order Alexander modules, but non-isomorphic nth-order linking forms. Furthermore, we define new higher-order linking forms on the Alexander modules for 3-manifolds considered by S. Harvey [H]. We construct examples of 3-manifolds with isomorphic nth-order Alexander modules, but non-isomorphic nth-order linking forms.en_US
dc.format.extent46 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH. 2004 LEIDYen_US
dc.identifier.citationLeidy, Constance. "Higher-order linking forms." (2004) Diss., Rice University. <a href="https://hdl.handle.net/1911/18660">https://hdl.handle.net/1911/18660</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/18660en_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.subjectMathematicsen_US
dc.titleHigher-order linking formsen_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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