knot theory

knot theory
noun Date: 1981 a branch of topology concerned with the properties and classification of mathematical knots • knot theorist noun

New Collegiate Dictionary. 2001.

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  • Crossing number (knot theory) — In the mathematical area of knot theory, the crossing number of a knot is the minimal number of crossings of any diagram of the knot. It is a knot invariant. By way of example, the unknot has crossing number zero, the trefoil knot three and the… …   Wikipedia

  • Mutation (knot theory) — The Kinoshita–Terasaka knot and the Conway knot respectively, and how they are related by mutation. In the mathematical field of knot theory, a mutation is an operation on a knot that can produce different knots. Suppose K is a knot given in the… …   Wikipedia

  • Physical knot theory — is the study of mathematical models of knotting phenomena, often motivated by physical considerations from biology, chemistry, and physics. Traditional knot theory models a knot as a simple closed loop in three dimensional space. Such a knot has… …   Wikipedia

  • Conway notation (knot theory) — Left: A tangle a and its reflection a. Top right: Tangle addition, denoted by a + b. Center right: Tangle product, denoted by a b, equivalent to a + b. Bottom right: Ramification, denoted by a , b, equivalent to a + b In knot theory, Conway… …   Wikipedia

  • Link (knot theory) — In mathematics, a link is a collection of knots which do not intersect, but which may be 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 …   Wikipedia

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