Victoria University

The Khovanov homology of knots

ResearchArchive/Manakin Repository

Show simple item record

dc.contributor.advisor Whittle, Geoff Le Gros, Giovanna 2015-12-11T00:06:02Z 2015-12-11T00:06:02Z 2015 2015
dc.description.abstract The Khovanov homology is a knot invariant which first appeared in Khovanov's original paper of 1999, titled ``a categorification of the Jones polynomial.'' This thesis aims to give an exposition of the Khovanov homology, including a complete background to the techniques used. We start with basic knot theory, including a definition of the Jones polynomial via the Kauffman bracket. Next, we cover some definitions and constructions in homological algebra which we use in the description of our title. Next we define the Khovanov homology in an analogous way to the Kauffman bracket, using only the algebraic techniques of the previous chapter, followed closely by a proof that the Khovanov homology is a knot invariant. After this, we prove an isomorphism of categories between TQFTs and Frobenius objects, which finally, in the last chapter, we put in the context of the Khovanov homology. After this application, we discuss some topological techniques in the context of the Khovanov homology. en_NZ
dc.language.iso en_NZ
dc.publisher Victoria University of Wellington en_NZ
dc.subject Knot invariant en_NZ
dc.subject Jones polynomial en_NZ
dc.subject Mathematics en_NZ
dc.title The Khovanov homology of knots en_NZ
dc.type Text en_NZ
vuwschema.contributor.unit School of Mathematics, Statistics and Operations Research en_NZ
vuwschema.contributor.unit Centre for Applied Cross-Cultural Research en_NZ
vuwschema.type.vuw Awarded Research Masters Thesis en_NZ Mathematics en_NZ Victoria University of Wellington en_NZ Masters en_NZ Master of Science en_NZ
dc.rights.license Author Retains All Rights en_NZ 2015-12-09T02:36:50Z
vuwschema.subject.anzsrcfor 010199 Pure Mathematics not elsewhere classified en_NZ
vuwschema.subject.anzsrcseo 970101 Expanding Knowledge in the Mathematical Sciences en_NZ
vuwschema.subject.anzsrctoa 1 PURE BASIC RESEARCH en_NZ

Files in this item

This item appears in the following Collection(s)

Show simple item record

Search ResearchArchive

Advanced Search


My Account