Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Jones polynomials and classical conjectures in knot theory. II

Kunio Murasugia1

a1 University of Toronto, Canada

Let L be an alternating link and S0305004100067335_inline1 be its reduced (or proper) alternating diagram. Let w(S0305004100067335_inline1) denote the writhe of S0305004100067335_inline1 [3], i.e. the number of positive crossings minus the number of negative crossings. Let VL(t) be the Jones polynomial of L [2]. Let dmax VL(t) and dmin VL(t) denote the maximal and minimal degrees of VL(t), respectively. Furthermore, let σ(L) be the signature of L [5].

(Received October 15 1986)