Separable and tree-like asymptotic cones of groups

Details Separable and tree-like asymptotic cones of groups Separable and tree-like asymptotic cones of groups

2010-10-06

arxiv.org/abs/1010.1199v2

Mathematics

Metric Geometry

The hypothesis of Theorem 1.2 had to be strengthened

Scientific paper

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.

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