Abstract

For every oriented link L in the 3-sphere there is a 2-variable Laurent polynomial PL(f, m ) ~ 7/[/? ±1, m±l]. It is defined uniquely by the formulae (i) Pv = 1 for the unknot U; (ii) ~?PL+ + e-XPL_ + mPL0 =0 , where L+, L_, and L0 are any three links identical except within a ball where they are as shown in Figure I. Details are given in [ F Y H L M O ] and [L-M 1]. This two-variable polynomial is related to At., the Alexander polynomial, and Vz., the Jones polynomial, by

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