Geometry of (1,1)-Knots and Knot Floer Homology

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datacite.rightsopen.access
dc.contributor.advisorSzabo, Zoltanen_US
dc.contributor.authorRacz, Bela Andrasen_US
dc.contributor.otherMathematics Departmenten_US
dc.date.accessioned2015-02-08T18:08:42Z
dc.date.accessioned2026-09-30T11:32:15Z
dc.date.available2015-02-08T18:08:42Z
dc.date.available2026-09-30T11:32:15Z
dc.date.issued2015en_US
dc.description.abstractWe apply the technique of Heegaard Floer Homology to (1,1)-knots (1-bridge knots on the torus) to determine all (1,1)-knots of crossing number up to 12. We also prove miscellaneous results regarding (1,1)-knots, including the existence of a family with trivial Alexander polynomial, and symmetry results. In addition, we define and study a new class of multi-pointed Heegaard diagrams for links in S^3 that generalizes the classical notion of grid diagrams.en_US
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/dsp01ft848s85j
dc.identifier.urihttps://theses-dissertations.princeton.edu/handle/88435/dsp01ft848s85j
dc.language.isoenen_US
dc.publisherPrinceton, NJ : Princeton Universityen_US
dc.relation.isformatofThe Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the <a href=http://catalog.princeton.edu> library's main catalog </a>en_US
dc.subject(1,1)-knotsen_US
dc.subjectgrid diagramsen_US
dc.subjectHeegaard Floer homologyen_US
dc.subjectknot invariantsen_US
dc.subject.classificationMathematicsen_US
dc.titleGeometry of (1,1)-Knots and Knot Floer Homologyen_US
dc.typeAcademic dissertations (Ph.D.)en_US
pu.projectgrantnumber690-2143en_US

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