Conway skein triple

Three oriented link diagrams, or tangle diagrams, $L_+$, $L_-$, $L_0$ in $\mathbf R^3$, or more generally, in any three-dimensional manifold, that are the same outside a small ball and in the ball look like

<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/c130240a.gif" />

Figure: c130240a

Similarly one can define the Kauffman bracket skein triple of non-oriented diagrams $L_+$, $L_0$ and $L_\infty$, and the Kauffman skein quadruple, $L_+$, $L_-$, $L_0$ and $L_\infty$, used to define the Brandt–Lickorish–Millett–Ho polynomial and the Kauffman polynomial:

<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/c130240b.gif" />

Figure: c130240b

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

References

[a1]	J.H. Conway, "An enumeration of knots and links" J. Leech (ed.), Computational Problems in Abstract Algebra , Pergamon (1969) pp. 329–358

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