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H. Bass has studied existence of lattices on trees. Can someone suggest a (readable) reference for lattices on graphs?

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group: what kinds of results are you looking for? I mean: every finitely generated group acts cocompactly on its Cayley graph and embeds (as a lattice if I'm not completely mistaken) into the locally compact automorphism group of that graph, so you can't expect any kind of structure theory à la Bass-Serre (and Bass-Lubotzky) in this generality. – t.b. Aug 31 '11 at 7:51
@Theo: If $\Gamma$ is acting on locally finite tree $X$. Then $\Gamma$ admits a lattice (a discrete subgroup with compact quotient, finite stabilizer) if $\Gamma$ is unimodular. So, we consider category of general (locally finite) graphs and do similar problems. – user8186 Aug 31 '11 at 8:04
Yes, of course, Bass's existence theorem is one of the deep results on tree lattices. I tried to point out to you that you can't expect to say anything sensible about lattices in groups of automorphisms of (locally finite) graphs without further restrictions (e.g. Gromov hyperbolicity) since otherwise you'll get all finitely generated groups. – t.b. Aug 31 '11 at 8:14

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