22 research outputs found
Noncoherence of some lattices in Isom(Hn)
We prove noncoherence of certain families of lattices in the isometry group
of the hyperbolic n-space for n greater than 3. For instance, every nonuniform
arithmetic lattice in SO(n,1) is noncoherent, provided that n is at least 6.Comment: This is the version published by Geometry & Topology Monographs on 29
April 2008. V3: typographical correction
Integral criteria of hyperbolicity for graphs and groups
We establish three criteria of hyperbolicity of a graph in terms of ``average
width of geodesic bigons''. In particular we prove that if the ratio of the Van
Kampen area of a geodesic bigon and the length of in the Cayley
graph of a finitely presented group is bounded above then is
hyperbolic.
We plan to use these results to characterize hyperbolic groups in terms of
random walks.Comment: 17 pages, 3 figure
The Martin boundary of relatively hyperbolic groups with virtually abelian parabolic subgroups
Given a probability measure on a finitely generated group, its Martin
boundary is a way to compactify the group using the Green's function of the
corresponding random walk. We give a complete topological characterization of
the Martin boundary of finitely supported random walks on relatively hyperbolic
groups with virtually abelian parabolic subgroups. In particular, in the case
of nonuniform lattices in the real hyperbolic space H n , we show that the
Martin boundary coincides with the CAT (0) boundary of the truncated space, and
thus when n = 3, is homeomorphic to the Sierpinski carpet