Pulling back the weight system associated with the exceptional Lie algebra g 2 by a modification of the universal Vassiliev-Kontsevich invariant yields a link invariant; extending it to 3-nets, we derive a recursive algorithm for its evaluation. Mathematics Subject Classification (1991). 57M25. It has been shown that the link invariants obtained from the classical simple Lie algebras sl n , so n , and sp n satisfy certain versions of the skein relation of the HOMFLY polynomial (sl n ; see [LM

more »

... ) resp. the Kauffman polynomial (so n , sp n ; see [LM 2]). But what about the exceptional simple Lie algebras? The authors are partially supported by the Schweizerische Nationalfonds. Vol. 75 (2000) The skein relation for the (g 2 , V )-link invariant 135 1 i.e. the vector field assigned to N consists of vectors pointing upward Vol. 75 (2000) The skein relation for the (g 2 , V )-link invariant 137 vector field assigned to M consists of vectors of the form (0, 0, 1). Remark 1.3. The overview in the introduction intimates that we will obtain an invariant of closed 3-nets that is composed of Vassiliev invariants (see also section 6). Vassiliev invariants are usually defined for oriented links, but we remind the reader that there is a definition for unoriented links (see e.g. [St]): A link invariant 2 f is a Vassiliev invariant of type m if for any link L, any diagram D(L) of L and any subset C of the set of crossings of D(L) with cardinality greater than m the following equation holds: X⊂C (−1) |X| f ([D(L) X ]) = 0, where |X| is the cardinality of X, D(L) X is the link diagram obtained form D(L) by changing all the crossings in X, and [D(L) X ] is a link with diagram D(L) X (such that the framing on the link is given by the blackboard framing of the diagram). Of course, this definition can be extended to 3-nets.