Year: 2024
Type: article
Abstract: There is a map, defined and studied by Jones, from Thompson’s group F to knots. Jones proved that every knot is in the image of this map — that is, that every knot can be seen as the “knot closure” of a Thompson group element. We approach the question of methodologically finding Thompson group elements to generate a particular knot or link through the lens of Conway’s rational tangles. We are able to give methods to construct any product or concatenation of simple tangles, and we hope these are seeds for a more skein-theoretic approach to the construction question.
Authors: Ariana Grymski, Emily Peters
Institutions: University of Wisconsin–Madison, Loyola University Chicago
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G2901713997
OpenAlex ID: W4403503776