Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

The skein polynomial of a planar star product of two links

Kunio Murasugia1 and Jozef H. Przytyckia2

a1 Department of Mathematics, University of Toronto, Toronto, Canada M5S 1A1

a2 Department of Mathematics, Warsaw University, Warsaw, Poland 00901

Abstract

If PL(v,z) = Σbi(v)zi is the skein polynomial of a link L, and D = D1 * D2 is the diagram which is a planar star (Murasugi) product of D1 and D2 then bϕ(D)(v) = bϕ(D1)·bϕ(D2)(v) where ϕ(D) = n(D)– (s(D) – 1) and n(D) denotes the number of crossings of D, and s(D) is the number of Seifert circles of D.

(Received July 11 1988)

(Revised October 24 1988)

(Online publication June 28 2011)