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{{DISPLAYTITLE:6₃ knot}} {{short description|Mathematical knot with crossing number 6}} ...

{{Short description|Minimum number of times a specific knot must be passed through itself to become untied}} [[Image:Unknotting trefoil.svg|300px|thumb|Trefoil knot without 3-fold symmetry being unknotted by one crossing switch.]] ...

[[Image:Blue 8_1 Knot.png|thumb|right|A twist knot with six half-twists.]] ...of knots, and are considered the simplest type of knots after the [[torus knot]]s. ...

In [[mathematics]], two [[link (knot theory)|links]] <math>L_0 \subset S^n</math> and <math>L_1 \subset S^n</mat == Concordance invariants == ...

{{Short description|Concept in mathematical knot theory}} ...ed Jones polynomial]] of [[Surgery theory|surgery]] presentations of the [[knot complement]].<ref name=rt91/><ref> ...

...lanar algebras provide an appropriate algebraic framework for other [[knot invariants]] in cases the elements involved in the computation are alternating. The co ...e property that states that the Jones Polynomial of an alternating [[Link (knot theory)|link]] is an alternating polynomial. ...

{{Short description|Group presentations useful in knot theory}} ...>\{g_1,g_2,\ldots,g_k\}.</math> [[Wilhelm Wirtinger]] observed that the [[knot complement|complements of knots]] in [[Three-dimensional space|3-space]] ha ...

{{Short description|Mathematical invariants used to classify plane curves}} ...the topology and geometry of [[plane curve|plane curves]]. The three main invariants—<math>J^+</math>, <math>J^-</math>, and <math>St</math>—provide ways to cla ...

{{Short description|Analog of the knot group}} ...heory)|link]] is an analog of the [[knot group]] of a [[Knot (mathematics)|knot]]. They were described by [[John Milnor]] in his Ph.D. thesis, {{harv|Milno ...

...curves with few crossings are likely to be tree-like, and therefore random knot diagrams with few crossings are likely to be unknotted.<ref>{{citation | title = Knot probabilities in random diagrams ...

{{Short description|Form of knot diagram}} ...|upright=1.2|Petal projection of a [[trefoil knot]], the unique nontrivial knot with petal number five{{r|acd}}]] ...

{{Short description|Conjecture in knot theory relating quantum invariants and hyperbolic geometry}} | field = [[Knot theory]] ...

...cs]], and for their use in constructing [[Knot invariant|invariants]] of [[knot theory|knots]], links, and three-dimensional [[manifolds]].<ref name="Baxte .../ref><ref name="Reshetikhin1991">Reshetikhin, N.Yu.; Turaev, V.G. (1991). "Invariants of 3-manifolds via link polynomials and quantum groups". ''[[Inventiones Ma ...

{{Infobox knot theory | last knot= L10a139 ...

...of Donaldson and Seiberg-Witten invariants) with links to gauge theory, [[knot theory]], and [[symplectic geometry]]. He works closely with [[Ronald J. St *with Stern: ''Donaldson invariants of 4-manifolds with simple type'', J. Diff. Geom., vol. 42, 1995, pp.&nbsp; ...

...one of the main problems in quantum topology has been to interpret quantum invariants topologically. ...lidis, M. Goussarov, and M. Polyak, ''Calculus of clovers and finite-type invariants of 3-manifolds'', Geom. and Topol., vol. 5 (2001), 75&ndash;108. ...

...] specializing in [[topology]], especially [[low-dimensional topology]], [[knot theory|the theory of knots and links]] and associated algebra. ...ce group]], whose lower levels encapsulate many classical knot concordance invariants. ...

...a knot is called a [[Gauss diagram]].{{r|pv94}} In the Gauss diagram of a knot, every chord crosses an even number of other chords, or equivalently each p | title = Gauss diagram formulas for Vassiliev invariants ...

{{Short description|Family of quantum invariants}} ...ikhin–Turaev invariants''' ('''RT-invariants''') are a family of [[quantum invariants]] of [[framed link]]s. ...

| known_for = [[Writhe]] of a knot<br/>Călugăreanu invariant ...uj.ro/~calu/59gauss.pdf}}</ref> he showed how to calculate the writhe of a knot by means of a Gaussian [[multiple integral|double integral]].<ref>{{cite jo ...