2008/06/19 by Silver, Daniel S., Whitten, Wilbur
#57M25 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)
paper · doi:10.48550/arxiv.0806.3223
We consider the relations ≥ and ≥p on the collection of all knots, where k ≥ k' (respectively, k ≥p k') if there exists an epimorphism πk → πk' of knot groups (respectively, preserving peripheral systems). When k is a torus knot, the relations coincide and k' must also be a torus knot; we determine the knots k' that can occur. If k is a 2-bridge knot and k ≥p k', then k' is a 2-bridge knot with determinant a proper divisor of the determinant of k; only finitely many knots k' are possible.