KNOT GROUP EPIMORPHISMS

Abstract

Let G be a finitely generated group, and let λ ∈ G. If there exists a knot k such that πk = π1(S3\k) can be mapped onto G sending the longitude to λ, then there exists infinitely many distinct prime knots with the property. Consequently, if πk is the group of any knot (possibly composite), then there exists an infinite number of prime knots k1, k2, … and epimorphisms ⋯ → πk2 → πk1 → πk each perserving peripheral structures. Properties of a related partial order on knots are discussed.