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May 20, 2012 at 1:44 comment added Ian Agol Right, I see, I should only consider cocompact actions.
May 19, 2012 at 14:48 comment added Misha @Ian: In this degree of generality, you will not get compactly generated groups. For instance, take an infinitely generated subgroup $G$ of a f.g. free group $F$ and let $G$ act on the tree which is the Cayley graph of $F$. So, I think you have to assume that $G$ acts on the set of triples in the Cantor set cocompactly, but not a priori discretely.
May 19, 2012 at 6:13 history edited Ian Agol CC BY-SA 3.0
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May 19, 2012 at 0:51 history edited Ian Agol CC BY-SA 3.0
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May 18, 2012 at 19:33 history answered Ian Agol CC BY-SA 3.0