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From Wikipedia, the free encyclopedia

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.

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Transcription

Contents

Properties

  • 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.

Examples

See also

Further reading

  • Kawauchi, A. A Survey of Knot Theory. Birkhauser.
This page was last edited on 25 March 2014, at 16:47.
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