We show that the Alexander-Conway polynomial is obtainable via a particular one-variable reduction of each two-variable Links–Gould invariant , where is a positive integer. Thus there exist infinitely many two-variable generalisations of . This result is not obvious since in the reduction, the representation of the braid group generator used to define does not satisfy a second-order characteristic identity unless . To demonstrate that the one-variable reduction of satisfies the defining skein relation of , we evaluate the kernel of a quantum trace.
"Infinitely many two-variable generalisations of the Alexander–Conway polynomial." Algebr. Geom. Topol. 5 (1) 405 - 418, 2005. https://doi.org/10.2140/agt.2005.5.405