Skip navigation
Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp017w62fb53x
 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. URI: http://arks.princeton.edu/ark:/88435/dsp017w62fb53x 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

Files in This Item:
File Description SizeFormat
Manion_princeton_0181D_11334.pdf1.33 MBAdobe PDF

Items in Dataspace are protected by copyright, with all rights reserved, unless otherwise indicated.