Universal lattices and property tau

  title={Universal lattices and property tau},
  author={Martin Kassabov and Nikolay Nikolov},
  journal={Inventiones mathematicae},
We prove that the universal lattices – the groups G=SLd(R) where R=ℤ[x1,...,xk], have property τ for d≥3. This provides the first example of linear groups with τ which do not come from arithmetic groups. We also give a lower bound for the τ-constant with respect to the natural generating set of G. Our methods are based on bounded elementary generation of the finite congruence images of G, a generalization of a result by Dennis and Stein on K2 of some finite commutative rings and a relative… Expand
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