H. Bass has studied existence of lattices on trees. Can someone suggest a (readable) reference for lattices on graphs?
Reference: Geometric group theory
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geometric-group-theory
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0group: 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. – 2011-08-31
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0@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. – 2011-08-31
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0Yes, 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. – 2011-08-31