Left Orderability of Cyclic Branched Covers of Rational Knots

dc.contributor.advisorTran, Anh
dc.contributor.advisorDieckmann, Gregg R.
dc.contributor.committeeMemberDabkowski, Mieczyslaw K.
dc.contributor.committeeMemberDragovic, Vladimir
dc.contributor.committeeMemberRamakrishna, Viswanath
dc.creatorMeyer, Bradley D 1993-
dc.date.accessioned2023-10-25T21:31:17Z
dc.date.available2023-10-25T21:31:17Z
dc.date.created2023-08
dc.date.issuedAugust 2023
dc.date.submittedAugust 2023
dc.date.updated2023-10-25T21:31:17Z
dc.description.abstractA non-trivial group G is left orderable if there is a total ordering < on G such that g < h implies f g < f h for all f, g, h ∈ G. In this dissertation, we study the left orderability of the fundamental groups of cyclic branched covers of the 3-sphere, S3, branched over rational knots. Specifically, the focus is on the three parameter family of rational knots C(2p, 2m, 2n+1) in the Conway notation. This study is motivated by the L-space conjecture of Boyer-Gordon-Watson, which states that an irreducible rational homology 3-sphere is an L-space if and only if its fundamental group is not left oderable. A sufficient condition for the fundamental group of the r-th cyclic branched cover of S3 branched over a prime knot to be left orderable was given by Hu in [12]. As an application, Turner determined the left orderability of the fundamental groups of the cyclic branched covers of the rational knots C(2n + 1, 2, 2) for a positive integer n. In Chapters 2 and 3, we generalize Turners results to the rational knots C(2p, 2m, 2n + 1) where p, m, n are integers.
dc.format.mimetypeapplication/pdf
dc.identifier.uri
dc.identifier.urihttps://hdl.handle.net/10735.1/9970
dc.language.isoEnglish
dc.subjectMathematics
dc.titleLeft Orderability of Cyclic Branched Covers of Rational Knots
dc.typeThesis
dc.type.materialtext
thesis.degree.collegeSchool of Natural Sciences and Mathematics
thesis.degree.departmentMathematics
thesis.degree.grantorThe University of Texas at Dallas
thesis.degree.namePHD

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