Asymptotic cones of finitely presented groups
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Let G be a connected semisimple Lie group with at least one absolutely simple factor S such that R-rank(S) is at least 2, and let $Γ$ be a uniform lattice in G.
(a) If $CH$ holds, then $Γ$ has a unique asymptotic cone up to homeomorphism.
(b) If $CH$ fails, then $Γ$ has $2^{2^ω}$ asymptotic cones up to homeomorphism.
To appear in Advances in Mathematics
To appear in Advances in Mathematics