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dc.contributor.advisorGordon, Cameron, 1945-
dc.creatorMoore, Allison Heatheren
dc.date.accessioned2013-10-23T17:35:48Zen
dc.date.issued2013-05en
dc.date.submittedMay 2013en
dc.identifier.urihttp://hdl.handle.net/2152/21684en
dc.descriptiontexten
dc.description.abstractIn this dissertation we prove that if an n-stranded pretzel knot K has an essential Conway sphere, then there exists an Alexander grading s such that the rank of knot Floer homology in this grading, [mathematical equation], is at least two. As a consequence, we are able to easily classify pretzel knots admitting L-space surgeries. We conjecture that this phenomenon occurs more generally for any knot in S³ with an essential Conway sphere. We also exhibit an infinite family of knots, each of which admits a nontrivial genus two mutant which shares the same total dimension of knot Floer homology, while being distinguished by knot Floer homology as a bigraded invariant. Additionally, the genus two mutation interchanges the [mathematical symbol]-graded knot Floer homology groups in [mathematical symbol]-gradings k and -k. This infinite family of examples supports a second conjecture, namely that the total rank of knot Floer homology is invariant under genus two mutation.en
dc.format.mimetypeapplication/pdfen
dc.language.isoen_USen
dc.subjectKnot theoryen
dc.subjectHeegaard Floer homologyen
dc.subjectPretzel knotsen
dc.subjectMutationen
dc.titleBehavior of knot Floer homology under conway and genus two mutationen
dc.date.updated2013-10-23T17:35:48Zen
dc.description.departmentMathematicsen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorThe University of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen


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