Unknot

Unknot

The unknot arises in the mathematical theory of knots. Intuitively, the unknot is a closed loop of rope without a knot in it. A knot theorist would describe the unknot as an image of any embedding that can be deformed, i.e. ambient-isotoped, to the standard unknot, i.e. the embedding of the circle as a geometrically round circle. The unknot is also called the trivial knot. An unknot is the identity element with respect to the knot sum operation.

Deciding if a particular knot is the unknot was a major driving force behind knot invariants, since it was thought this approach would possibly give an efficient algorithm to recognize the unknot from some presentation such as a knot diagram. Currently there are several well-known unknot recognition algorithms (not using invariants), but they are either known to be inefficient or have no efficient implementation. It is not known whether the current invariants, such as finite type invariants, are a complete invariant of the unknot. Even if they were, the problem of computing them efficiently remains.

Many useful practical knots are actually the unknot, including all knots which can be tied in the bight.cite web|url=http://www.volkerschatz.com/knots/knots.html|title=Knotty topics|author=Volker Schatz|accessdate=2007-04-23]

ee also

*Knot (mathematics)
*Unknotting problem
*Unlink

References


Wikimedia Foundation. 2010.

Игры ⚽ Поможем сделать НИР

Look at other dictionaries:

  • Unknot — Un*knot , v. t. [1st un + knot.] To free from knots; to untie. [1913 Webster] …   The Collaborative International Dictionary of English

  • unknot — index break (separate), disengage, disentangle, extricate Burton s Legal Thesaurus. William C. Burton. 2006 …   Law dictionary

  • unknot — [unnät′] vt. unknotted, unknotting 1. to untie (a knot) 2. to undo or untangle a knot or knots in …   English World dictionary

  • unknot — /un not /, v.t., unknotted, unknotting. to untie by or as if by undoing a knot: to unknot a tie. [1590 1600; UN 2 + KNOT1] * * * …   Universalium

  • unknot — 1. noun /ˈʌnːɒt/lang=en In knot theory, a loop that is not knotted. 2. verb /ˈʌnːɒt/lang=en To undo (a knot). See Also: disentangle, untangle, untie …   Wiktionary

  • unknot — v. untie a knot, loosen a knot, unfasten a string or rope that has been tied …   English contemporary dictionary

  • unknot — verb (unknots, unknotting, unknotted) release or untie the knot or knots in …   English new terms dictionary

  • unknot — un·knot …   English syllables

  • unknot — un•knot′ v. t. knot•ted, knot•ting …   From formal English to slang

  • unknot — v.tr. (unknotted, unknotting) release the knot or knots of, untie …   Useful english dictionary

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”