Working on my thesis project. Given two torsion-free groups $$\Gamma_1,\Gamma_2$$ which are elementarily equivalent and both hyperbolic relative to their abelian subgroups, I'm currently trying to determine what sorts of constraints I can put on how homomorphisms $$\Gamma_1\to\Gamma_2$$ behave on the abelian subgroups.

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@_c_perez ooh, lovely bit of geometric group theory

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