CONJUGATE GENERATORS OF KNOT AND LINK GROUPS

Abstract

This note establishes a stronger version of a conjecture of Reid and others in the arithmetic case: if two elements of equal trace (e.g. conjugate elements) generate an arithmetic two-bridge knot or link group, then the elements are parabolic (and hence peripheral). This includes the figure-eight knot and Whitehead link groups. Similarly, if two conjugate elements generate the trefoil knot group, then the elements are peripheral.