Behavior of knot Floer homology under conway and genus two mutation

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.date.updated2013-10-23T17:35:48Zen
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.description.departmentMathematicsen
dc.format.mimetypeapplication/pdfen
dc.identifier.urihttp://hdl.handle.net/2152/21684en
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
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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