Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01qz20ss65q
 Title: Higher Differentials on Khovanov Homology Authors: Seed, Cotton Advisors: Szabo, Zoltan Contributors: Mathematics Department Keywords: differentialhomologyKhovanovknotspectral sequencetopology Subjects: Mathematics Issue Date: 2014 Publisher: Princeton, NJ : Princeton University Abstract: In 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. URI: http://arks.princeton.edu/ark:/88435/dsp01qz20ss65q Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog Type of Material: Academic dissertations (Ph.D.) Language: en Appears in Collections: Mathematics

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