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Colin Conrad Adams (born October 13, 1956) is an American mathematician primarily working in the areas of hyperbolic 3-manifolds and knot theory.His book, The Knot Book, has been praised for its accessible approach to advanced topics in knot theory.
Download as PDF; Printable version; In other projects ... The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots, ... (1997), An Introduction ...
A few major discoveries in the late 20th century greatly rejuvenated knot theory and brought it further into the mainstream. In the late 1970s William Thurston's hyperbolization theorem introduced the theory of hyperbolic 3-manifolds into knot theory and made it of prime importance. In 1982, Thurston received a Fields Medal, the highest honor ...
Three-twist knot is the twist knot with three-half twists, also known as the 5 2 knot. Trefoil knot A knot with crossing number 3; Unknot; Knot complement, a compact 3 manifold obtained by removing an open neighborhood of a proper embedding of a tame knot from the 3-sphere. Notation used in knot theory: Conway notation
Lickorish and Kenneth Millett won the 1991 Chauvenet Prize for their paper "The New Polynomial Invariants of Knots and Links". [3] Lickorish was included in the 2019 class of fellows of the American Mathematical Society "for contributions to knot theory and low-dimensional topology". [4]
Many knot polynomials are computed using skein relations, which allow one to change the different crossings of a knot to get simpler knots.. In the mathematical field of knot theory, a knot polynomial is a knot invariant in the form of a polynomial whose coefficients encode some of the properties of a given knot.
A central question in the mathematical theory of knots is whether two knot diagrams represent the same knot. One tool used to answer such questions is a knot polynomial, which is computed from a diagram of the knot and can be shown to be an invariant of the knot, i.e. diagrams representing the same knot have the same polynomial. The converse ...
A knot diagram with crossings labelled for a Dowker sequence. In the mathematical field of knot theory, the Dowker–Thistlethwaite (DT) notation or code, for a knot is a sequence of even integers. The notation is named after Clifford Hugh Dowker and Morwen Thistlethwaite, who refined a notation originally due to Peter Guthrie Tait. [1]
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