Knot theory is a rich topic in topology that studies the how circles can be embedded in Euclidean 3-space. One of the main questions in knot theory is how to distinguish between different types of knots efficiently. One way to approach this problem is to study knot invariants, which are properties of knots that do not change under a standard set of deformations. We give a brief overview of basic knot theory, and examine a specific knot invariant known as Khovanov homology. Khovanov homology is a homological invariant that refines the Jones polynomial, another knot invariant that assigns a Laurent polynomial to a knot. Dror Bar-Natan wrote a paper in 2002 that explains the construction of Khovanov homology and proves that it is an invariant. We follow his lead and attempt to clarify and explain his formulation in more precise detail.
| Identifer | oai:union.ndltd.org:CALPOLY/oai:digitalcommons.calpoly.edu:theses-4390 |
| Date | 01 December 2023 |
| Creators | Liu, Shiaohan |
| Publisher | DigitalCommons@CalPoly |
| Source Sets | California Polytechnic State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Master's Theses |
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