Non-rectifiable Delone sets in SOL and other solvable groups

الأصل · EN

Given a lattice Γ⊂ SOL, we show that there is a coarsely dense subset D ⊂ Γ that is not biLipschitz equivalent to Γ. We also prove similar results for lattices in certain higher rank abelian-by-abelian groups and for the solvable Baumslag-Solitar groups.