82 research outputs found
On Bestvina-Mess Formula
Bestvina and Mess [BM] proved a remarkable formula for torsion free
hyperbolic groups connecting the
cohomological dimension of a group with the cohomological dimension of
its boundary . In [Be] Bestvina introduced a notion of
\sZ-structure on a discrete group and noticed that his formula holds true for
all torsion free groups with \sZ-structure. Bestvina's notion of
\sZ-structure can be extended to groups containing torsion by replacing the
covering space action in the definition by the geometric action. Though the
Bestvina-Mess formula trivially is not valid for groups with torsion, we show
that it still holds in the following modified form: {\it The cohomological
dimension of a \sZ-boundary of a group equals its global
cohomological dimension for every PID as the coefficient group} Using this formula we show that
the cohomological dimension of the boundary is a
quasi-isometry invariant of a group.Comment: 10 page
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