Relation between triples of links differing by 1 crossing, used to compute knot invariants
Skein relations are a mathematical tool used to study knots. A central question in the mathematical theory of knots is whether two knot diagrams represent the same knot. One way to answer the question is using knot polynomials, which are invariants of the knot. If two diagrams have different polynomials, they represent different knots. However, the converse is not true.
Skein relations are often used to give a simple definition of knot polynomials. A skein relation gives a linear relation between the values of a knot polynomial on a collection of three links which differ from each other only in a small region. For some knot polynomials, such as the Conway, Alexander, and Jones polynomials, the relevant skein relations are sufficient to calculate the polynomial recursively.
converse is not true. Skein relations are often used to give a simple definition of knot polynomials. A skeinrelation gives a linear relation between the values...
themselves Skein module, a mathematical concept Skeinrelation, a mathematical concept often used to give a simple definition of knot polynomials Skein (comics)...
now called the Alexander–Conway polynomial, could be computed using a skeinrelation, although its significance was not realized until the discovery of the...
computation using a skeinrelation. It computes the Alexander–Conway polynomial of the trefoil knot. The yellow patches indicate where the relation is applied...
the value 1 on any diagram of the unknot and satisfies the following skeinrelation: ( t 1 / 2 − t − 1 / 2 ) V ( L 0 ) = t − 1 V ( L + ) − t V ( L − ) {\displaystyle...
following explanation for the relation to knot polynomials from the view point of Khovanov homology. The skeinrelation for three links L 1 , L 2 {\displaystyle...
a skeinrelation for a version of the Alexander polynomial, usually referred to as the Alexander–Conway polynomial. The significance of this skein relation...
flowers of plants in the genus Potentilla. Pentagram Trefoil knot 7₁ knot Skeinrelation Weisstein, Eric W. "Solomon's Seal Knot". MathWorld. A Pentafoil Knot...
knot Hyperbolic link Knot invariants Crossing number Linking number Skeinrelation Knot polynomials Alexander polynomial Jones polynomial Knot group Writhe...
circular loop surrounding the crossing of the figure-eight. The above-below relation between these two unknots is then set as an alternating link, with the...
around each circle; another equivalent way to describe the over-under relation between the three circles is that each circle passes over a second circle...
Global Information