Links - Infinitely many two-variable generalisations of the Alexander-Conway polynomial

Abstract We show that the Alexander-Conway polynomial ∆ is obtain-able via a particular one-variable reduction of each two-variable Links– Gould invariant LGm,1, where m is a positive integer. Thus there exist infinitely many two-variable generalisations of ∆. This result is not obvi-ous since in the reduction, the representation of the braid group generator used to define LGm,1 does not satisfy a second-order characteristic identity unless m = 1. To demonstrate that the one-variable reduction of LGm,1 satisfies the defining skein relation of ∆, we evaluate the kernel of a quan-tum trace. AMS Classification 57M25, 57M27; 17B37, 17B8