Conway-Alexander polynomial

The Alexander polynomial is a knot invariant discovered in 1923 by J. W. Alexander. The Alexander polynomial remained the only known knot polynomial until the Jones polynomial was discovered in 1984. Unlike the Alexander polynomial, the more powerful Jones polynomial does, in most cases, distinguish handedness. In technical language, the Alexander polynomial arises from the homology of the infinitely cyclic cover of a knot complement. Any generator of a principal Alexander ideal is called an Alexander polynomial. Because the Alexander invariant of a tame knot in S^3 has a square presentation matrix, its Alexander ideal is principal and it has an Alexander polynomial denoted Δ(t).

braid group | Conway polynomial | Jones polynomial | knot | knot determinant | link | link crossing number | skein relationship