Quandles, n-Colorability, and Cocycles

File(s)
Date
2024-04Author
Heuss, Sarah
Advisor(s)
Davis, Christopher
Metadata
Show full item recordAbstract
In the 1960s Ralph Fox introduced a tool of knot theory called colorability. Briefly, a knot is n-colorable if the diagram for that knot can be decorated with numbers 1, 2, . . . , n subject to a simple constraint at each crossing. Whether or not a diagram of a knot admits an n-coloring turns out to be independent of the diagram. Thus, one can attempt to distinguish knots by asking if they admit n-colorable diagrams. In this project, we study n-colorings of n-colorable knots. In particular if one colors a single knot diagram in two different ways then when can these seemingly distinct colorings be said to be deformed into each other? On the way, we use tools from the theory of quandles including Alexander quandles and cocycle enhancements.
Subject
Knot theory
Colorability
Posters
Department of Mathematics
Permanent Link
http://digital.library.wisc.edu/1793/94438Type
Presentation
Description
Color poster with text, charts, and diagrams.