Symmetries of knots, branched cyclic covers, and L-spaces

dc.contributor.advisorGordon, Cameron, 1945-
dc.contributor.committeeMemberBoyer, Steven
dc.contributor.committeeMemberDanciger, Jeffrey
dc.contributor.committeeMemberLuecke, John
dc.creatorTurner, Hannah Kathryn
dc.date.accessioned2022-01-27T18:43:38Z
dc.date.available2022-01-27T18:43:38Z
dc.date.created2021-08
dc.date.issued2021-08
dc.date.submittedAugust 2021
dc.date.updated2022-01-27T18:43:39Z
dc.description.abstractThis dissertation studies the L-space conjecture among manifolds which are branched cyclic covers of links. We present three main results. First, we construct new families of knots all of whose branched cyclic covers are L-spaces. Then, we give an almost complete characterization of which cyclic branched covers of double-twist knots have left-orderable fundamental groups. Finally, we relate the notion of visibility of certain symmetries of an alternating knot to the Heegaard Floer homology of its cyclic branched covers.
dc.description.departmentMathematics
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/2152/95657
dc.identifier.urihttp://dx.doi.org/10.26153/tsw/22573
dc.language.isoen
dc.subjectTopology
dc.subjectL-space conjecture
dc.titleSymmetries of knots, branched cyclic covers, and L-spaces
dc.typeThesis
dc.type.materialtext
thesis.degree.departmentMathematics
thesis.degree.disciplineMathematics
thesis.degree.grantorThe University of Texas at Austin
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

Access full-text files

Original bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
TURNER-DISSERTATION-2021.pdf
Size:
548.38 KB
Format:
Adobe Portable Document Format

License bundle

Now showing 1 - 2 of 2
No Thumbnail Available
Name:
PROQUEST_LICENSE.txt
Size:
4.45 KB
Format:
Plain Text
Description:
No Thumbnail Available
Name:
LICENSE.txt
Size:
1.84 KB
Format:
Plain Text
Description: