Bounded geometry in relatively hyperbolic groups
نویسنده
چکیده
If a group is relatively hyperbolic, the parabolic subgroups are virtually nilpotent if and only if there exists a hyperbolic space with bounded geometry on which it acts geometrically finitely. This provides, via the embedding theorem of M. Bonk and O. Schramm, a very short proof of the finiteness of asymptotic dimension for such groups (which is known to imply Novikov conjectures).
منابع مشابه
N ov 2 00 4 Bounded geometry in relatively hyperbolic groups
We prove that a group is hyperbolic relative to virtually nilpotent subgroups if and only if there exists a Gromov-hyperbolic metric space with bounded geometry on which it acts as a relatively hyperbolic group. As a consequence we obtain that any group hyperbolic relative to virtually nilpotent subgroups has finite asymptotic dimension. For these groups the Novikov conjecture holds. The class ...
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تاریخ انتشار 2004