Abstract:We introduce the notion of graphical discreteness to group theory. A finitely generated group is graphically discrete if whenever it acts geometrically on a locally finite graph, the automorphism group of the graph is compact-by-discrete. Notable examples include finitely generated nilpotent groups, most lattices in semisimple Lie groups, and irreducible non-geometric 3-manifold groups. We show graphs of groups with graphically discrete vertex groups frequently have strong rigidity properties. We prove free pr… Show more
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