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RECOVERING LINK DATA FROM THE B-GRAPH OF AN ALTERNATING DIAGRAM

In this paper we study ways in which link data may be recovered from the B-graph G of an alternating link diagram D of link L. In particular we find explicitly the coefficients of the three-variable backet (Kauffman square bracket) of D in terms of the Tutte polynomial of G. We go on to show how both polynomials capture the twist number of alternating 2-bridge and 3-braid link diagrams. Finally, we discuss the open questions of recovering the signature of L (when L is a knot) or the first homology group of the double cover of S branched over L from G.