Tree Lattices
Let X be a locally finite tree. Then the automorphism group G of X is a locally compact topological group, in which the basis of the topology is given by the stabilizers of finite sets of vertices. Vertex stabilizers Gx are thus compact open subgroups, and a subgroup Γ of G is discrete if Γx is finite for some (and hence, for any) vertex x. The subgroup Γ is an X-lattice if the suitably defined volume of is finite, and a uniform X-lattice if this quotient is a finite graph. In case is finite, this is equivalent to Γ being a lattice (respectively, a uniform lattice) in G.
Read more about this topic: Lattice (discrete Subgroup)
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