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Title: Constructions and Computations in Khovanov Homology
Authors: Manion, Andrew
Advisors: Szabo, Zoltan
Contributors: Mathematics Department
Subjects: Mathematics
Issue Date: 2015
Publisher: Princeton, NJ : Princeton University
Abstract: In 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.
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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