Conway Polynomial


The Conway Polynonial (or Alexander-Conway polynomial) ΔL(z) of an oriented link L is given by det(z1/2A - z-1/2At), where A is a Seifert Matrix for L.

It can be shown that the Conway Polynomial is determined by the following skein relations:

(1) ΔUnknot(z) = 1

(2) ΔL+(z) - ΔL-(z) = zΔL0(z),

where L+, L-, and L0 are three oriented links which are the same except in a neighborhood of a point where they differ as in the figure below.

Conway Polynomial Skein Relations

References

[1] Lickorish, W. B. R., An introduction to knot theory. New York: Springer (1997).

[2] Image taken from Wikipedia, The Free Encyclopedia. Alexander Polynomial.