Geometric group actions on trees

We define geometric group actions on [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]-trees, as dual to a measured foliation on a 2-complex with some finiteness and injectivity properties. We prove that an action is nongeometric if and only if it is a nontrivial strong limit in the sense of Gillet-Shalen. We give a simple new construction of the Bass-Serre tree of a graph of groups, and we show that a simplicial action is geometric if and only if edge groups are finitely generated. We prove that geometric actions with trivial edge stabilizers have finitely many orbits of branch points, and finite rank.