Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01w37639528
 Title: Khovanov Homology and Mutation Authors: Hickok, Abigail Advisors: Ozsvath, PeterSzabo, Zoltan Department: Mathematics Class Year: 2018 Abstract: Khovanov homology is a knot invariant that categorifies the Jones polynomial. In Chapter 1, we will go through the construction of Khovanov homology, and survey some of its connections to knot Floer homology. In Chapter 2, we will discuss the conjecture that Khovanov homology is invariant under Conway mutation. We will consider two independent proofs of the fact that Khovanov homology over $\mathbb{F}_2$ is mutation invariant. Finally, in Chapter 3, we will look at the behavior of Khovanov homology under cabled mutation, which is a generalization of Conway mutation and a special case of genus-2 mutation. URI: http://arks.princeton.edu/ark:/88435/dsp01w37639528 Type of Material: Princeton University Senior Theses Language: en Appears in Collections: Mathematics, 1934-2020