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Unknotting problem information


Unsolved problem in mathematics:

Can unknots be recognized in polynomial time?

(more unsolved problems in mathematics)
Two simple diagrams of the unknot
A tricky unknot diagram by Morwen Thistlethwaite

In mathematics, the unknotting problem is the problem of algorithmically recognizing the unknot, given some representation of a knot, e.g., a knot diagram. There are several types of unknotting algorithms. A major unresolved challenge is to determine if the problem admits a polynomial time algorithm; that is, whether the problem lies in the complexity class P.

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Unknotting problem

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problem in mathematics: Can unknots be recognized in polynomial time? (more unsolved problems in mathematics) In mathematics, the unknotting problem is...

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Unknotting

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Unknotting may refer to: Unknotting number, the minimum number of times the knot must be passed through itself to untie it Unknotting problem, a mathematical...

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Unknot

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Intuitively, the unknot is a closed loop of rope without a knot tied into it, unknotted. To a knot theorist, an unknot is any embedded topological circle in the...

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List of unsolved problems in mathematics

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of Ravenel's conjectures in stable homotopy theory to be resolved. Unknotting problem: can unknots be recognized in polynomial time? Volume conjecture relating...

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Disentanglement puzzle

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which is found in some disentanglement puzzles Human knot Tangloids Unknotting problem Unlink Horak, Matthew (2006). "Disentangling Topological Puzzles by...

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Unknotting number

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Trefoil knot unknotting number 1 Figure-eight knot unknotting number 1 Cinquefoil knot unknotting number 2 Three-twist knot unknotting number 1 Stevedore...

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Open Problems in Mathematics

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Few Remarks, by Peter Constantin Plateau’s Problem, by Jenny Harrison and Harrison Pugh The Unknotting Problem, by Louis Kauffman How Can Cooperative Game...

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Knot theory

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understand how hard this problem really is (Hass 1998). The special case of recognizing the unknot, called the unknotting problem, is of particular interest...

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Human knot

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to try to untangle the knot. Not all human knots are solvable (see unknotting problem) and can remain knots or may end up as two or more circles. An easy...

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List of knot theory topics

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Temperley–Lieb algebra Thurston–Bennequin number Tricolorability Unknotting number Unknotting problem Volume conjecture Schubert's theorem Conway's theorem Alexander's...

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Wolfgang Haken

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Hermann Haken, a physicist known for laser theory and synergetics. Unknotting problem Werner Haken, Beitrag zur Kenntnis der thermoelektrischen Eigenschaften...

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Knot tabulation

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matter of days. Knot theory Knot (mathematics) List of prime knots Unknotting problem Hoste, Jim; Thistlethwaite, Morwen; Weeks, Jeff (1998), "The first...

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Joel Hass

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special case of the double bubble conjecture, for proving that the unknotting problem is in NP, and for giving an exponential bound on the number of Reidemeister...

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Linkless embedding

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is equivalent in complexity to unknotting problem, the problem of testing whether a single curve in space is unknotted. Testing unknottedness (and therefore...

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Pachner moves

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but the isomorphism does not preserve the triangulation. Flip graph Unknotting problem Pachner, Udo (1991), "P.L. homeomorphic manifolds are equivalent by...

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Trefoil knot

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HOMFLY Jones Kauffman Pretzel Prime list Stick no. Tricolorability Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation...

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74 knot

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HOMFLY Jones Kauffman Pretzel Prime list Stick no. Tricolorability Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation...

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Tait conjectures

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HOMFLY Jones Kauffman Pretzel Prime list Stick no. Tricolorability Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation...

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Alternating knot

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HOMFLY Jones Kauffman Pretzel Prime list Stick no. Tricolorability Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation...

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Borromean rings

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Unsolved problem in mathematics: Are there three unknotted curves, not all circles, that cannot form the Borromean rings? (more unsolved problems in mathematics)...

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Reidemeister move

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Lagarias, Jeffrey C. (2001), "The number of Reidemeister moves needed for unknotting", Journal of the American Mathematical Society, 14 (2): 399–428, arXiv:math/9807012...

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Whitehead link

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HOMFLY Jones Kauffman Pretzel Prime list Stick no. Tricolorability Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation...

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Writhe

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HOMFLY Jones Kauffman Pretzel Prime list Stick no. Tricolorability Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation...

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Hyperbolic link

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HOMFLY Jones Kauffman Pretzel Prime list Stick no. Tricolorability Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation...

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Knot complement

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HOMFLY Jones Kauffman Pretzel Prime list Stick no. Tricolorability Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation...

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Braid group

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braid groups. The word problem is also efficiently solved via the Lawrence–Krammer representation. In addition to the word problem, there are several known...

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Alexander polynomial

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p. 150. Kawauchi credits this result to Kondo, H. (1979), "Knots of unknotting number 1 and their Alexander polynomials", Osaka J. Math. 16: 551-559...

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