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• 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
• 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
• 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
• 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
• Unknotting number (category Knot invariants) (section Other numerical knot invariants)
  determined. (The unknotting number of the 1011 prime knot is unknown.) Crossing number Bridge number Linking number Stick number Unknotting problem Adams
  4 KB (379 words) - 22:25, 6 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
• 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
• 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
• 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
• Topology (category Articles with Curlie links) (section Continuous functions and homeomorphisms)
  engineering and materials science. Electrical and mechanical properties depend on the arrangement and network structures of molecules and elementary units
  35 KB (4,033 words) - 17:48, 6 February 2024
• Knot tabulation (category Knot theory)
  with three crossings (the minimum for any nontrivial knot), the number of prime knots for each number of crossings is 1, 1, 2, 3, 7, 21, 49, 165, 552, 2176
  5 KB (564 words) - 15:24, 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
• 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
• 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
• Link group (category Knot invariants)
  invariants, and in fact they (and their products) are the only rational finite type concordance invariants of string links; (Habegger Masbaum). The number of linearly
  9 KB (1,196 words) - 14:58, 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
• 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
• Unknotting problem (category Knot theory)
  co-NP. Knot Floer homology of the knot detects the genus of the knot, which is 0 if and only if the knot is an unknot. A combinatorial version of knot Floer
  11 KB (1,220 words) - 22:16, 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
• 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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