Unlink

Unlink

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 "D""i" ⊂ S3 such that "L" = ∪"i"∂"D""i".
* A link with one component is an unlink if and only if it is isotopic to the unknot.
* 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 two-component unlink.
* Kanenobu has shown that for all "n" > 1 there exists a hyperbolic link of "n" components such that any proper sublink is an unlink. The Whitehead link and Borromean rings are such examples for "n" = 2, 3.

ee also

*Unknot
*Link (knot theory)
*Linking number


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Look at other dictionaries:

  • Unlink — Un*link , v. t. [1st pref. un + link.] To separate or undo, as links; to uncoil; to unfasten. Shak. [1913 Webster] …   The Collaborative International Dictionary of English

  • unlink — index detach Burton s Legal Thesaurus. William C. Burton. 2006 …   Law dictionary

  • unlink — [unliŋk′] vt. 1. to unfasten the links of (a chain, etc.) 2. to separate (things linked together) …   English World dictionary

  • unlink — /un lingk /, v.t. 1. to separate the links of (a chain, linked bracelet, watchband, etc.); unfasten. 2. to detach or separate by or as if by undoing one or more connecting links: to unlink hands. v.i. 3. to become detached. [1590 1600; UN 2 +… …   Universalium

  • unlink — un•link [[t]ʌnˈlɪŋk[/t]] v. t. 1) to separate the links of (a chain, bracelet, etc.); unfasten 2) to detach or release as if by undoing a link or links: to unlink hands[/ex] 3) to become detached …   From formal English to slang

  • Unlink (Unix) — In Unix like operating systems, unlink is a system call and a command line utility to delete files. The program directly interfaces the system call, which removes the file name and (but not on GNU systems) directories like rm and rmdir. If the… …   Wikipedia

  • unlink — Date: 1600 transitive verb to unfasten the links of ; separate, disconnect intransitive verb to become detached …   New Collegiate Dictionary

  • unlink — verb a) To decouple an item; to remove a link; to delink. b) To delete a file …   Wiktionary

  • unlink — verb separate; detach …   English new terms dictionary

  • unlink — un·link …   English syllables

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