Unlink  

2component unlink


Common name  Circle 
Crossing no.  0 
Linking no.  0 
Stick no.  6 
Unknotting no.  0 
Conway notation   
AB notation  02 1 
Dowker notation   
Next  L2a1 
Other  
, tricolorable (if n>1) 
Look up unlink in Wiktionary, the free dictionary. 
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 ncomponent link L ⊂ S^{3} is an unlink if and only if there exists n disjointly embedded discs D_{i} ⊂ S^{3} such that L = ∪_{i}∂D_{i}.
 A link with one component is an unlink if and only if it is the unknot.
 The link group of an ncomponent unlink is the free group on n generators, and is used in classifying Brunnian links.
Examples
 The Hopf link is a simple example of a link with two components that is not an unlink.
 The Borromean rings form a link with three components that is not an unlink; however, any two of the rings considered on their own do form a twocomponent unlink.
 Kanenobu^{[who?]} has shown that for all n > 1 there exists a hyperbolic link of n components such that any proper sublink is an unlink (a Brunnian link). The Whitehead link and Borromean rings are such examples for n = 2, 3.^{[full citation needed]}
See also
Further reading
 Kawauchi, A. A Survey of Knot Theory. Birkhauser.
This page was last edited on 25 March 2014, at 16:47.