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• Unknot (category Non-alternating knots and links)
  seen as a trivial knot In the mathematical theory of knots, the unknot, not knot, or trivial knot, is the least knotted of all knots. Intuitively, the
  5 KB (560 words) - 19:08, 6 February 2024
• (−2,3,7) pretzel knot (category Non-alternating knots and links)
  (−2, 3, 7) pretzel knot has 7 exceptional slopes, Dehn surgery slopes which give non-hyperbolic 3-manifolds. Among the enumerated knots, the only other hyperbolic
  2 KB (138 words) - 20:13, 6 February 2024
• Knot theory (category Knot theory) (section Adding knots)
  The knot sum of oriented knots is commutative and associative. A knot is prime if it is non-trivial and cannot be written as the knot sum of two non-trivial
  48 KB (6,198 words) - 19:12, 6 February 2024
• Borromean rings (category Alternating knots and links) (section Definition and notation)
  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
• Figure-eight knot (mathematics) (category Alternating knots and links)
  generalizing Thurston's construction to other knots and links. The figure-eight knot is also the hyperbolic knot whose complement has the smallest possible
  9 KB (986 words) - 18:54, 6 February 2024
• Alternating knot (category Knot invariants)
  characterization of alternating links in terms of definite spanning surfaces, i.e. a definition of alternating links (of which alternating knots are a special
  6 KB (693 words) - 16:41, 6 February 2024
• Whitehead link (category Alternating knots and links)
  two unknots is then set as an alternating link, with the consecutive crossings on each loop alternating between under and over. This drawing has five crossings
  6 KB (622 words) - 16:01, 6 February 2024
• Link (knot theory) (section Tangles, string links, and braids)
  linked (or knotted) together. A knot can be described as a link with one component. Links and knots are studied in a branch of mathematics called knot theory
  8 KB (1,104 words) - 22:45, 6 February 2024
• Tait conjectures (category Knot theory) (section Crossing number of alternating knots)
  to all knots, or just to alternating knots. It turns out that most of them are only true for alternating knots. In the Tait conjectures, a knot diagram
  6 KB (672 words) - 14:48, 6 February 2024
• Hyperbolic link (redirect from Hyperbolic knot) (category Hyperbolic knots and links)
  three-twist knot) 61 knot (the stevedore knot) 62 knot 63 knot 74 knot 10 161 knot (the "Perko pair" knot) 12n242 knot SnapPea Hyperbolic volume (knot) Colin
  2 KB (228 words) - 15:55, 6 February 2024
• Jones polynomial (category Knot theory) (section Link with quantum knot invariants)
  constructed a certain chain complex for knots and links and showed that the homology induced from it is a knot invariant (see Khovanov homology). The Jones
  17 KB (2,344 words) - 19:41, 6 February 2024
• Prime knot (category Knot invariants)
  it is a non-trivial knot which cannot be written as the knot sum of two non-trivial knots. Knots that are not prime are said to be composite knots or composite
  3 KB (288 words) - 21:40, 6 February 2024
• L10a140 link (category Alternating 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
• Carrick mat (category Alternating knots and links)
  flat, it can be used as a woggle. List of knots Budworth, Geoffrey (1999). The Ultimate Encyclopedia of Knots & Ropework. London: Hermes House. p. 227. 
  3 KB (213 words) - 00:14, 7 February 2024
• List of mathematical knots and links (category Knot theory) (section Knots)
  mathematical knots and links. See also list of knots, list of geometric topology topics. 01 knot/Unknot - a simple un-knotted closed loop 31 knot/Trefoil knot
  3 KB (419 words) - 17:53, 8 February 2024
• Bridge number (category Knot invariants)
  decomposed into two trivial n-tangles and hence 2-bridge knots are rational knots. If K is the connected sum of K1 and K2, then the bridge number of K is one
  3 KB (366 words) - 22:55, 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
• 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
• 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
• Braid group (category Knot theory) (section Generators and relations)
  \Z }[/math], and [math]\displaystyle{ B_3 }[/math] is isomorphic to the knot group of the trefoil knot – in particular, it is an infinite non-abelian group
  36 KB (4,579 words) - 15:02, 6 February 2024

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