The Jones polynomial of parallels and applications to crossing number

Richard Andrew Stong

Vol. 164 (1994), No. 2, 383–395

DOI: 10.2140/pjm.1994.164.383

Abstract

In this paper we study the Jones polynomial of the parallels of a link or knot. From the extremal exponents occurring we derive lower bounds on the crossing number of the knot, reproducing in particular a number of results of Thistlethwaite. We apply these techniques to give lower bound on the crossing number of some simple satellites of adequate and semi-adequate knots (including cable satellites) that are usually quadratic in the degree of the satellite.

Mathematical Subject Classification 2000

Primary: 57M25

Milestones

Received: 15 September 1990

Revised: 24 July 1991

Published: 1 June 1994