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Mar 29, 2013 at 15:21 vote accept Michael Siler
Mar 22, 2013 at 14:27 answer added Misha timeline score: 8
Mar 22, 2013 at 2:10 comment added Misha First, assume the holonomy group of your manifold is nonelementary and that the manifold is complete. Now the geom finite statement holds. Second, assume that fundamental group is finitely generated and the manifold is geom infinite. Then Thurston's covering theorem gives complete answer.
Mar 22, 2013 at 0:41 history asked Michael Siler CC BY-SA 3.0