Conjugate Generators of Knot and Link Groups

Abstract

This note shows that if two elements of equal trace (e.g., conjugate elements) generate an arithmetic two-bridge knot or link group, then the elements are parabolic. 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.

10 pages, submitted to Journal of Knot Theory and Its Ramifications