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dc.contributor.advisorSzabo, Zoltanen_US
dc.contributor.authorSeed, Cottonen_US
dc.contributor.otherMathematics Departmenten_US
dc.description.abstractIn this thesis, we study the structure and geometric content of Khovanov homology using higher differentials. We study the Szabo geometric spectral sequence and conjecture that it agrees with the spectral sequence from Khovanov homology to the Heegaard Floer homology of the double-branched cover of a knot. We define a twisted variant of the geometric spectral sequence, connect it to Baldwin-Ozsvath-Szabo homology, and outline a strategy towards the above conjecture. We construct a new spectral sequence that begins at the Khovanov homology of a link and converges to the Khovanov homology of the disjoint union of its components. The page at which the spectral sequence collapses gives a lower bound on the splitting number of the link, the minimum number of times its components must be passed through one another in order to completely separate them. In addition, we build on work of Kronheimer-Mrowka and Hedden-Ni to show that Khovanov homology detects the unlink.en_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=> library's main catalog </a>en_US
dc.subjectspectral sequenceen_US
dc.titleHigher Differentials on Khovanov Homologyen_US
dc.typeAcademic dissertations (Ph.D.)en_US
Appears in Collections:Mathematics

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