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The solvable Baumslag Solitar groups BS (1, n) each admit a canonical model space, Xₙ. We give a complete classification of lattices in Gₙ = Isom^+ (Xₙ) and find that such lattices fail to be strongly rigidx2014there are automorphisms of lattices Gₙ which do not extend to Gₙx2014but do satisfy a weaker form of rigidity: for all isomorphic lattices ₁, ₂ Gₙ, there is an automorphism Aut (Gₙ) so that (₁) = ₂.
Noah Caplinger (Fri,) studied this question.