Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Seifert circles and knot polynomials

H. R. Mortona1

a1 Department of Pure Mathematics, University of Liverpool

In this paper I shall show how certain bounds on the possible diagrams presenting a given oriented knot or link K can be found from its two-variable polynomial PK defined in [3]. The inequalities regarding exponent sum and braid index of possible representations of K by a closed braid which are proved in [5] and [2] follow as a special case.

(Received April 24 1985)