Asymptotic cones of finitely presented groups
Abstract
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.