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Separable and tree-like asymptotic cones of groups
Using methods from nonstandard analysis, we will discuss which metric spaces
can be realized as asymptotic cones. Applying the results we will find in the
context of groups, we will prove that a group with "a few" separable asymptotic
cones is virtually nilpotent, and we will classify the real trees appearing as
asymptotic cones of (not necessarily hyperbolic) groups.Comment: The hypothesis of Theorem 1.2 had to be strengthene
Asymptotic cones of finitely presented groups
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 be a uniform
lattice in G.
(a) If holds, then has a unique asymptotic cone up to
homeomorphism.
(b) If fails, then has asymptotic cones up to
homeomorphism.Comment: To appear in Advances in Mathematic
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