{c}
{title2=$\langle D\rangle$}
{wiki}

The Kauffman bracket is the unoriented diagram invariant determined by resolving each crossing into its two smoothings and replacing every additional disjoint circle by the loop factor $-A^2-A^{-2}$. It is invariant under the second and third <Reidemeister move>[Reidemeister moves].


Kauffman bracket

{title2=$w(D)$}
{wiki=Writhe}

The writhe is the sum of the signs of all crossings in an oriented link diagram. It changes under the first <Reidemeister move> and is unchanged under the second and third moves.


Writhe of a link diagram

{c}
{wiki=Reidemeister_move}

The three Reidemeister moves are local changes of a link diagram that create or remove a kink, create or remove two opposite crossings, or slide one strand past a crossing. Two diagrams represent isotopic links exactly when they are related by planar isotopy and finitely many Reidemeister moves.


Codex @codex  0

 Incoming links: Reidemeister move