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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
  • Torus knot (category Wikipedia articles needing page number citations from November 2017) (section g-torus knot)
    Topology and Its Applications 33 (3): 241–246. doi:10.1016/0166-8641(89)90105-3.  "36 Torus Knots", The Knot Atlas. Weisstein, Eric W.. "Torus Knot". http://mathworld
    16 KB (1,682 words) - 22:31, 6 February 2024
  • Alexander polynomial (category Knot theory)
    (1990). Knots and Links (2nd ed.). Publish or Perish. ISBN 978-0-914098-16-4.  (explains classical approach using the Alexander invariant; knot and link table
    17 KB (2,507 words) - 19:35, 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
  • Ribbon knot (category Knots and links)
    slice-ribbon conjecture for 3-stranded pretzel knots", American Journal of Mathematics 133 (3): 555–580, doi:10.1353/ajm.2011.0022 . On Knots, Annals of Mathematics
    5 KB (564 words) - 22:35, 6 February 2024
  • Seifert surface (redirect from Knot genus) (category Knot theory) (section Existence and Seifert matrix)
    [math]\displaystyle{ v(i, j) }[/math] the linking number in Euclidean 3-space (or in the 3-sphere) of ai and the "pushoff" of aj in the positive direction
    10 KB (1,330 words) - 23:42, 6 February 2024
  • Carrick mat (category 3 braid number knots and links)
    Ultimate Encyclopedia of Knots & Ropework. London: Hermes House. p. 227.  Ashley, Clifford W. (1944). The Ashley Book of Knots. New York: Doubleday. pp
    3 KB (213 words) - 00:14, 7 February 2024
  • Braid group (category Knot theory) (section Relation between B3 and the modular group)
    theorem in 3-manifolds", Topology and Its Applications 78 (1–2): 95–122, doi:10.1016/S0166-8641(96)00151-4  Birman, Joan S. (1974), Braids, links, and mapping
    36 KB (4,579 words) - 15:02, 6 February 2024
  • Knot tabulation (category Knot theory)
    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, 9988, 46972
    5 KB (564 words) - 15:24, 6 February 2024
  • Pretzel link (category 3-manifolds)
    pretzel knot is a non-invertible knot. The (2p, 2q, 2r) pretzel link is a link formed by three linked unknots. The (−3, 0, −3) pretzel knot (square knot (mathematics))
    7 KB (920 words) - 22:53, 6 February 2024
  • Arf invariant of a knot (category Knot invariants) (section Arf as knot concordance invariant)
    either the unknot or the trefoil; these two knots are not pass-equivalent and additionally, the right- and left-handed trefoils are pass-equivalent. Now we
    5 KB (682 words) - 18:43, 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
  • 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
  • Writhe (category Knot theory)
    segments numbered [math]\displaystyle{ i }[/math] and [math]\displaystyle{ j }[/math], number the endpoints of the two segments 1, 2, 3, and 4. Let [math]\displaystyle{
    10 KB (1,359 words) - 14:58, 6 February 2024
  • Linking number (category Knot invariants) (section Computing the linking number)
    total number of negative crossings is equal to twice the linking number. That is: [math]\displaystyle{ \text{linking number}=\frac{n_1 + n_2 - n_3 - n_4}{2}
    16 KB (2,349 words) - 19:45, 6 February 2024
  • Unknotting problem (category 3-manifolds)
    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)
    [D][−n−]{n+ − 2n−}, where n− denotes the number of left-handed crossings in the chosen diagram for D, and n+ the number of right-handed crossings. The Khovanov
    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
  • Conway sphere (category Knot theory)
    in knot theory In mathematical knot theory, a Conway sphere, named after John Horton Conway, is a 2-sphere intersecting a given knot or link in a 3-manifold
    2 KB (194 words) - 17:53, 8 February 2024

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