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2-component unlink
Common name Circle
Crossing no. 0
Linking no. 0
Stick no. 6
Unknotting no. 0
Conway notation -
A-B notation 02
Dowker notation -
Next L2a1
, tricolorable (if n>1)

In the mathematical field of knot theory, the unlink is a link that is equivalent (under ambient isotopy) to finitely many disjoint circles in the plane.


  • An n-component link L ⊂ S3 is an unlink if and only if there exists n disjointly embedded discs Di ⊂ S3 such that L = ∪iDi.
  • A link with one component is an unlink if and only if it is the unknot.
  • The link group of an n-component unlink is the free group on n generators, and is used in classifying Brunnian links.


See also[edit]

Further reading[edit]

  • Kawauchi, A. A Survey of Knot Theory. Birkhauser.