Geodesic
Cofinitely Hopfian groups, open mappings and knot complements
Martin R. Bridson1 orcid ; Daniel Groves2 orcid ; Jonathan A. Hillman3 ; Gaven J. Martin4 orcid
1University of Oxford, UK
2University of Illinois at Chicago, United States
3The University of Sydney, Australia
4Massey University, Auckland, New Zealand
Groups, geometry, and dynamics, Tome 4 (2010) no. 4, pp. 693-707

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DOI

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.
DOI : 10.4171/ggd/101
Classification : 20-XX, 57-XX, 00-XX
Mots-clés : Cofinitely Hopfian, open mappings, relatively hyperbolic, free-by-cyclic, knot groups

Martin R. Bridson  1   ; Daniel Groves  2   ; Jonathan A. Hillman  3   ; Gaven J. Martin  4

1 University of Oxford, UK
2 University of Illinois at Chicago, United States
3 The University of Sydney, Australia
4 Massey University, Auckland, New Zealand 
Martin R. Bridson; Daniel Groves; Jonathan A. Hillman; Gaven J. Martin. Cofinitely Hopfian groups, open mappings and knot complements. Groups, geometry, and dynamics, Tome 4 (2010) no. 4, pp. 693-707. doi: 10.4171/ggd/101
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     title = {Cofinitely {Hopfian} groups, open mappings and knot complements},
     journal = {Groups, geometry, and dynamics},
     pages = {693--707},
     year = {2010},
     volume = {4},
     number = {4},
     doi = {10.4171/ggd/101},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/101/}
}
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