No abstract

No abstract

Let G be a real centre-free semisimple Lie group without compact factors. I prove that irreducible lattices in G are rigid under two types of sublinear distortions. I show that if Λ ≤ G is a discrete subgroup that sublinearly covers a lattice, then Λ is itself a lattice. I use this result to prove that the class of lattices in groups that do not admit R-rank 1 factors is SBE complete: if Λ is an abstract finitely generated group that is Sublinearly BiLipschitz Equivalent (SBE) to a lattice in G, then Λ can be homomorphically mapped into G with finite kernel and image a lattice in G. This generalizes the well known quasi-isometric completeness of lattices in semisimple Lie groups.