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dc.contributor.advisorSzabo, Zoltanen_US
dc.contributor.authorManion, Andrewen_US
dc.contributor.otherMathematics Departmenten_US
dc.description.abstractIn this thesis, we present a collection of results relating to Khovanov homology. We consider the family of 3-strand pretzel links, and compute their unreduced and reduced Khovanov homology using two different methods. We also show how to extend Lawrence Roberts’ totally twisted Khovanov homology to integer coefficients, yielding a spanning tree model for odd Khovanov homology with an explicitly computable differential. Finally, we show that Khovanov’s functor-valued invariant of tangles contains the same information as Bar-Natan’s dotted cobordism tangle theory, and we construct a natural bordered theory for Khovanov homology using this invariant.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.titleConstructions and Computations in Khovanov Homologyen_US
dc.typeAcademic dissertations (Ph.D.)en_US
Appears in Collections:Mathematics

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