Quandles are algebraic gadgets introduced by David Joyce in  which can be used to define invarients of links. In the case of knots these invarients are complete up to equivalence, that is up to mirror images.
It is useful to consider as ’ acting on ’.
Let be some group, and let be some fixed integer. Then let .
Let be some group. Then let .
Let be some module, and some invertable linear operator on . Then let
Homomorphisms, isomorphisms etc. are defined in the obvious way. Notice that the third axiom gives us that the operation of a quandle element on the quandle given by is a homomorphism, and the second axiom ensures that this is an isomorphism.
- 1 D.Joyce : A Classifying Invariant Of Knots, The Knot Quandle : J.P.App.Alg 23 (1982) 37-65
|Date of creation||2013-03-22 16:42:37|
|Last modified on||2013-03-22 16:42:37|
|Last modified by||StevieHair (1420)|