A note on Morton's conjecture concerning the lowest degree of a $2$-variable knot polynomial

Peter Richard Cromwell

Vol. 160 (1993), No. 2, 201–205

DOI: 10.2140/pjm.1993.160.201

Abstract

This note is concerned with the behaviour of the ‘HOMFLY’ polynomial of oriented links, $P_L(v,z)$. In particular, we show that the gap between the two lowest powers of $v$ can be made arbitrarily large. This casts doubt on whether Morton’s conjecture on the least $v$-degree can be established in general by the kind of combinatorial approach that has been successfully applied to some special cases.

Mathematical Subject Classification

Primary: 57M25

Milestones

Received: 1 July 1991

Revised: 24 August 1992

Published: 1 October 1993