Arbitrary Real Volumes, Cusps, and Homology
Let X be a locally finite tree and Γ a non-uniform-lattice. In this section we show that, even when X is regular (of degree ≥ 3), Vol(Γ\\X) can take any positive real value ((4.3)), that Γ\X can have any conceivable number of “cusps” ((4.13) and (4.16)), and that these phenomena can occur with π1 (Γ\X) either finitely or infinitely generated. If we drop regularity, then every locally finite connected graph can occur as some Γ\X ((4.17)).
KeywordsParabolic Subgroup Tree Lattice Regular Tree Finite Subgroup Finite Graph
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