Conway skein triple

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Three oriented link diagrams, or tangle diagrams, , , in , or more generally, in any three-dimensional manifold, that are the same outside a small ball and in the ball look like

Figure: c130240a

Similarly one can define the Kauffman bracket skein triple of non-oriented diagrams , and , and the Kauffman skein quadruple, , , and , used to define the Brandt–Lickorish–Millett–Ho polynomial and the Kauffman polynomial:

Figure: c130240b

Generally, a skein set is composed of a finite number of -tangles and can be used to build link invariants and skein modules (cf. also Skein module).


[a1] J.H. Conway, "An enumeration of knots and links" J. Leech (ed.) , Computational Problems in Abstract Algebra , Pergamon (1969) pp. 329–358
How to Cite This Entry:
Conway skein triple. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by Jozef Przytycki (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article