Non-minimal tree actions and the existence of non-uniform tree lattices
2004 ◽
Vol 70
(2)
◽
pp. 257-266
Keyword(s):
A uniform tree is a tree that covers a finite connected graph. Let X be any locally finite tree. Then G = Aut(X) is a locally compact group. We show that if X is uniform, and if the restriction of G to the unique minimal G-invariant subtree X0 ⊆ X is not discrete then G contains non-uniform lattices; that is, discrete subgroups Γ for which Γ/G is not compact, yet carries a finite G-invariant measure. This proves a conjecture of Bass and Lubotzky for the existence of non-uniform lattices on uniform trees.
Keyword(s):
1989 ◽
Vol 32
(1)
◽
pp. 64-73
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Keyword(s):
2021 ◽
Vol 12
(1)
◽
2003 ◽
Vol 10
(3)
◽
pp. 503-508
◽
Keyword(s):
2017 ◽
Vol 28
(10)
◽
pp. 1750067
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1988 ◽
Vol 40
(1)
◽
pp. 109-111
◽
1992 ◽
Vol 12
(2)
◽
pp. 283-295
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