Cofinitely Hopfian Groups, Open Mappings and Knot Complements

Abstract

A group Γ is defined to be cofinitely Hopfian if every homomorphism Γ → Γ whose image is of finite index is an automorphism. Geometrically significant groups enjoying this property include certain relatively hyperbolic groups and many lattices. A knot group is cofinitely Hopfian if and only if the knot is not a torus knot. A free-by-cyclic group is cofinitely Hopfian if and only if it has trivial centre. Applications to the theory of open mappings between manifolds are presented.

Cite this paper

@inproceedings{Bridson2009CofinitelyHG, title={Cofinitely Hopfian Groups, Open Mappings and Knot Complements}, author={Martin R. Bridson and Gaven J. Martin}, year={2009} }