Knot Theory, Quandles, and Link Homotopy

Accessibility notice: If you need help accessing this archived item, Ask a Librarian.

dc.contributor.advisor	Davis, Christopher
dc.contributor.author	Darnall, Kiera
dc.contributor.author	Phillips, Nathan
dc.contributor.author	Weston, Briar
dc.date.accessioned	2026-04-01T14:55:09Z
dc.date.available	2026-04-01T14:55:09Z
dc.date.issued	2025-04
dc.identifier.uri	http://digital.library.wisc.edu/1793/97274
dc.description	Color poster with text and images.	en_US
dc.description.abstract	Knot Theory, Link Homotopy, and QuandlesIn the 1950s Milnor defined the notion of link homotopy. Since then, its study has been central to the field of knot theory. In the 1980s, Joyce, building on the work of Takasaki, defined a mathematical object called a quandle which is well adapted to the transformation of knot theoretic questions into algebraic questions. Trivial orbit quandles, defined in 2007 by Harrell and Nelson, are a type of quandle useful for studying link homotopy. In this poster, we define a new trivial orbit quandle called the reduced free quandle, and we go about classifying it for 2 and 3 generators. This gives classification of 2 and 3 component links up to link homotopy.	en_US
dc.description.sponsorship	University of Wisconsin--Eau Claire Office of Research and Sponsored Programs	en_US
dc.language.iso	en_US	en_US
dc.relation.ispartofseries	USGZE AS589;
dc.subject	Knot theory	en_US
dc.subject	Homology theory	en_US
dc.subject	Quandles	en_US
dc.subject	Posters	en_US
dc.subject	Department of Mathematics	en_US
dc.title	Knot Theory, Quandles, and Link Homotopy	en_US
dc.type	Presentation	en_US