Add to ORKGThere are many papers that introduce the relationship between knots and quandles which are written tersely and focus mainly on applications or implications. Here, we will take time to explain in depth how to derive quandles from oriented knots. Starting with an rigorous introduction to what a knot is and what a quandle is, we will also define the Fundamental Quandle of a knot and the relationship between colorings of a knot and the homomorphisms from an arbitrary quandle to a Fundamental Quandle. Then using this foundation, we will examine two sets of knots that produce quandles that contain subquandles and the set of quandles created by non-oriented knots
We show that the isomorphism problems for left distributive algebras, racks, quandles and kei are as...
If A is an abelian quandle and Q is a quandle, the hom set Hom(Q,A) of quandle homomorphisms from Q ...
AbstractWe introduce the concept of the quandle partial derivatives, and use them to define extreme ...
From prehistory to the present, knots have been used for purposes both artistic and practical. The m...
Quandles, which are algebraic structures related to knots, can be used to color knot diagrams, and t...
In this thesis we first give an introduction to knots, knot diagrams, and algebraic structures defin...
Knot theory has rapidly expanded in recent years. New representations of braid groups led to an extr...
AbstractThe two operations of conjugation in a group, x▷y=y-1xy and x▷-1y=yxy-1 satisfy certain iden...
A quandle is a set with a binary operation that satisfies three axioms that corresponds to the three...
Quandles are distributive algebraic structures originally introduced independently by David ...
Quandles are distributive algebraic structures that were introduced by David Joyce [24] in his P...
We show that the fundamental quandle defines a functor from the oriented tangle category to a suitab...
The thesis deal with coloring knots by algebraical structures called quandles. We will introduce the...
To better understand the fundamental quandle of a knot or link, it can be useful to look at finite q...
AbstractIn this paper we describe three geometric applications of quandle homology. We show that it ...
We show that the isomorphism problems for left distributive algebras, racks, quandles and kei are as...
If A is an abelian quandle and Q is a quandle, the hom set Hom(Q,A) of quandle homomorphisms from Q ...
AbstractWe introduce the concept of the quandle partial derivatives, and use them to define extreme ...
From prehistory to the present, knots have been used for purposes both artistic and practical. The m...
Quandles, which are algebraic structures related to knots, can be used to color knot diagrams, and t...
In this thesis we first give an introduction to knots, knot diagrams, and algebraic structures defin...
Knot theory has rapidly expanded in recent years. New representations of braid groups led to an extr...
AbstractThe two operations of conjugation in a group, x▷y=y-1xy and x▷-1y=yxy-1 satisfy certain iden...
A quandle is a set with a binary operation that satisfies three axioms that corresponds to the three...
Quandles are distributive algebraic structures originally introduced independently by David ...
Quandles are distributive algebraic structures that were introduced by David Joyce [24] in his P...
We show that the fundamental quandle defines a functor from the oriented tangle category to a suitab...
The thesis deal with coloring knots by algebraical structures called quandles. We will introduce the...
To better understand the fundamental quandle of a knot or link, it can be useful to look at finite q...
AbstractIn this paper we describe three geometric applications of quandle homology. We show that it ...
We show that the isomorphism problems for left distributive algebras, racks, quandles and kei are as...
If A is an abelian quandle and Q is a quandle, the hom set Hom(Q,A) of quandle homomorphisms from Q ...
AbstractWe introduce the concept of the quandle partial derivatives, and use them to define extreme ...