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Algorithmic and Geometric Topics Around Free Groups and Automorphisms
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This volume contains the lecture notes of the three summer courses given by the authors during the program "Automorphisms of Free Groups: Geometry, Topology, and Dynamics", held at the Centre de Recerca Matemŕtica (CRM) in Bellaterra (Barcelona).
The first two chapters present the basic tools from formal language theory (regular and context-free languages, automata, rewriting systems, transducers, etc) and emphasize their connections to group theory, mostly relating to free and virtually-free groups. The material covered is enough to present full proofs of many of the existing interesting characterizations of virtually-free groups.
The last chapter describes, in a comprehensive exposition, Bonahon's construction of Thurston's compactification of Teichmüller space, in terms of geodesic currents on surfaces. It also includes several interesting extensions of the notion of geodesic current to various other more general settings.
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