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arXiv · 1012.1785

Cofinitely Hopfian groups, open mappings and knot complements

Martin R. Bridson·Daniel Groves·Jonathan A. Hillman·Gaven J. Martin
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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 cofinitely Hopfian if and only if it has trivial centre. Applications to the theory of open mappings between manifolds are presented.

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Martin R. Bridson, Daniel Groves, Jonathan A. Hillman, Gaven J. Martin. 2010-12-08. Cofinitely Hopfian groups, open mappings and knot complements. https://doi.org/10.4171/ggd/101

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