Conjugate Generators of Knot and Link Groups

Details Conjugate Generators of Knot and Link Groups Conjugate Generators of Knot and Link Groups

2008-06-20

arxiv.org/abs/0806.3452v2

Mathematics

Geometric Topology

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

Scientific paper

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.

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