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• Jones polynomial (category Knot theory) (section Link with quantum knot invariants)
   175. ISBN 978-0-387-98254-0. https://www.springer.com/mathematics/geometry/book/978-0-387-98254-0.  Thistlethwaite, Morwen (2001). "Links with trivial Jones
  17 KB (2,344 words) - 19:41, 6 February 2024
• Borromean rings (category 6 crossing number knots and links) (section Number theory)
  In the tables of knots and links in Dale Rolfsen's 1976 book Knots and Links, extending earlier listings in the 1920s by Alexander and Briggs, the Borromean
  42 KB (4,468 words) - 20:52, 8 February 2024
• Dowker notation (category Knot theory) (section Uniqueness and counting)
  Dowker notation is unchanged by these reflections. Knots tabulations typically consider only prime knots and disregard chirality, so this ambiguity does not
  3 KB (343 words) - 14:41, 6 February 2024
• 2-bridge knot (category Knot theory)
  nontrivial knot. Other names for 2-bridge knots are rational knots, 4-plats, and Viergeflechte for 'four braids'. 2-bridge links are defined similarly as above
  3 KB (302 words) - 15:24, 6 February 2024
• Hyperbolic volume (category Knot theory) (section Knot and link invariant)
  complement is a knot invariant. In order to make it well-defined for all knots or links, the hyperbolic volume of a non-hyperbolic knot or link is often
  6 KB (626 words) - 21:17, 6 February 2024
• Knot polynomial (category Knot invariants) (section Specific knot polynomials)
  List of prime knots.) Alexander polynomials and Conway polynomials can not recognize the difference of left-trefoil knot and right-trefoil knot. The left-trefoil
  6 KB (439 words) - 17:42, 6 February 2024
• L10a140 link (category 3 braid number knots and links)
  the second in an infinite series of Brunnian links beginning with the Borromean rings. So if the blue and yellow loops have only one twist along each side
  6 KB (831 words) - 17:40, 6 February 2024
• Ribbon knot (category Knots and links)
  the conjecture is true for knots of bridge number two. (Greene Jabuka) showed it to be true for three-stranded pretzel knots with odd parameters. However
  5 KB (564 words) - 22:35, 6 February 2024
• Crosscap number (category Knot invariants) (section Knot sum)
  "Crosscaps and Knots", Int. J. Math and Math. Sci, Vol 1, 1978, pp 113–124 Murakami, Hitoshi and Yasuhara, Akira. "Crosscap number of a knot," Pacific J
  2 KB (212 words) - 18:46, 6 February 2024
• Conway sphere (category Knot theory)
  with unknotting number 1 and essential Conway spheres". Algebraic & Geometric Topology 6 (5): 2051–2116. doi:10.2140/agt.2006.6.2051. Bibcode: 2006math...
  2 KB (194 words) - 17:53, 8 February 2024
• Torus knot (category Wikipedia articles needing page number citations from November 2017) (section g-torus knot)
   [page needed]. ISBN 0-691-08065-8.  Rolfsen, Dale (1976). Knots and Links. Publish or Perish, Inc.. p. [page needed]. ISBN 0-914098-16-0.  Hill, Peter (December
  16 KB (1,682 words) - 22:31, 6 February 2024
• Alexander polynomial (category Knot theory)
  relation in 1970. Alexander, J.W. (1928). "Topological Invariants of Knots and Links". Transactions of the American Mathematical Society 30 (2): 275–306
  17 KB (2,507 words) - 19:35, 6 February 2024
• Arf invariant of a knot (category Knot invariants) (section Arf as knot concordance invariant)
  University Press. ISBN 0-691-08336-3.  Kauffman, Louis H. (1987). On knots. Annals of Mathematics Studies. 115. Princeton University Press. ISBN 0-691-08435-1. 
  5 KB (682 words) - 18:43, 6 February 2024
• Seifert surface (redirect from Knot genus) (category Knot theory) (section Existence and Seifert matrix)
  + 1 and Seifert matrix [math]\displaystyle{ V' = V \oplus \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}. }[/math] The genus of a knot K is the knot invariant
  10 KB (1,330 words) - 23:42, 6 February 2024
• Pretzel link
  is the connected sum of two trefoil knots. The (0, q, 0) pretzel link is the split union of an unknot and another knot. A Montesinos link is a special kind
  7 KB (920 words) - 22:53, 6 February 2024
• Writhe (category Knot theory)
  coils that increase its writhing number”. DNA supercoiling Linking number Ribbon theory Twist (mathematics) Winding number Bates, Andrew (2005). DNA Topology
  10 KB (1,359 words) - 14:58, 6 February 2024
• Braid group (category Knot theory) (section Generators and relations)
  v=\begin{bmatrix}0 & 1 \\ -1 & 0 \end{bmatrix}, \qquad p=\begin{bmatrix}0 & 1 \\ -1 & 1 \end{bmatrix}. }[/math] Mapping a to v and b to p yields a surjective
  36 KB (4,579 words) - 15:02, 6 February 2024
• Khovanov homology (category Knot invariants) (section The relation to link (knot) polynomials)
  [ø] = 0 → Z → 0, where ø denotes the empty link. [O D] = V ⊗ [D], where O denotes an unlinked trivial component. [D] = F(0 → [D0] → [D1]{1} → 0) In the
  11 KB (1,333 words) - 16:33, 6 February 2024
• Linking number (category Knot invariants) (section Computing the linking number)
  give the same number, so the linking number doesn't depend on any particular link diagram. This formulation of the linking number of γ1 and γ2 enables an
  16 KB (2,349 words) - 19:45, 6 February 2024
• Tricolorability (category Knot invariants) (section In torus knots)
  Accessed: May 5, 2013. Gilbert, N.D. and Porter, T. (1994) Knots and Surfaces, p. 8 Bestvina, Mladen (February 2003). "Knots: a handout for mathcircles", Math
  5 KB (646 words) - 00:14, 7 February 2024

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