Grothendieck’s problem for 3-manifold groups

  • Darren D. Long

    University of California, Santa Barbara, USA
  • Alan W. Reid

    University of Texas at Austin, USA


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The following problem was posed by Grothendieck:

Let be a homomorphism of finitely presented residually finite groups for which the extension is an isomorphism. Is an isomorphism?

The problem was solved in the negative by Bridson and Grunewald who produced many examples of groups and proper subgroups for which is an isomorphism, but is not.

This paper addresses Grothendieck’s problem in the context of 3-manifold groups.

Cite this article

Darren D. Long, Alan W. Reid, Grothendieck’s problem for 3-manifold groups. Groups Geom. Dyn. 5 (2011), no. 2, pp. 479–499

DOI 10.4171/GGD/135