Infinitely many two-variable generalisations of the Alexander-Conway polynomial
نویسندگان
چکیده
We show that the Alexander-Conway polynomial ∆ is obtainable via a particular one-variable reduction of each two-variable Links– Gould invariant LG , where m 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 LG does not satisfy a second-order characteristic identity unless m = 1. To demonstrate that the one-variable reduction of LG satisfies the defining skein relation of ∆, we evaluate the kernel of a quantum trace. AMS Classification 57M25, 57M27; 17B37, 17B81
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