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Cofinitely Hopfian groups, open mappings and knot complements (with
M. Bridson,
J. Hillman and
G. Martin).
.pdf (172k)
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** Abstract **
A group $\Gamma$ is defined to be cofinitely Hopfian if every homomorphism
$\Gamma \to \Gamma$ 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 confinitely Hopfian if and only if it has a trivial center.
Applications to the theory of open mappings between manifolds are presented.