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dc.contributor.advisorStover, Matthew
dc.creatorMorris, Timothy Michael
dc.date.accessioned2020-11-04T16:57:26Z
dc.date.available2020-11-04T16:57:26Z
dc.date.issued2019
dc.identifier.urihttp://hdl.handle.net/20.500.12613/3308
dc.description.abstractLet K be a tame knot embedded in S³. We address the problem of finding the minimal degree non-cyclic cover p : X → S³ \ K. When K has non-trivial Alexander polynomial we construct finite non-abelian representations p : π1 (S³\ K) → G, and provide bounds for the order of G in terms of the crossing number of K, which is an improvement on a result of Broaddus in this case. Using classical covering space theory along with the theory of Alexander stratifications we establish an upper and lower bound for the first betti number of the cover Xp associated to the ker (p) of S³ \ K, consequently showing that it can be arbitrarily large, which provides an effective proof of a result involving peripheral subgroup separation. We also demonstrate that Xp contains non-peripheral homology for certain computable examples, which mirrors a famous result of Cooper, Long, and Reid when K is a knot with non-trivial Alexander polynomial.
dc.format.extent61 pages
dc.language.isoeng
dc.publisherTemple University. Libraries
dc.relation.ispartofTheses and Dissertations
dc.rightsIN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available.
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectMathematics
dc.titleSome Non-abelian Covers of Knot Complements
dc.typeText
dc.type.genreThesis/Dissertation
dc.contributor.committeememberFuter, David
dc.contributor.committeememberPetersen, Kathleen
dc.contributor.committeememberTaylor, Samuel J.
dc.description.departmentMathematics
dc.relation.doihttp://dx.doi.org/10.34944/dspace/3290
dc.ada.noteFor Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
dc.description.degreePh.D.
refterms.dateFOA2020-11-04T16:57:26Z


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