In the study of knot group epimorphisms, the existence of an epimorphism between two given knot groups is mostly (if not always) shown by giving an epimorphism which preserves meridians. A natural question arises: is there an epimorphism preserving meridians whenever a knot group is a homomorphic image of another? We answer in the negative by presenting infinitely many pairs of prime knot groups.(G; G’) such that G’ is a homomorphic image of G but no epimorphism of G onto G’ preserves meridians.
- Knot groups
- Twisted Alexander polynomials