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This volume presents the lecture notes from the authors' three
summer courses offered during the program "Automorphisms of Free
Groups: Geometry, Topology, and Dynamics," held at the Centre de
Recerca Matematica (CRM) in Bellaterra, Spain. The first two
chapters present the basic tools needed, 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 sufficient to present full proofs of many of
the existing interesting characterizations of virtually-free
groups. In turn, the last chapter comprehensively describes
Bonahon's construction of Thurston's compactification of
Teichmuller space in terms of geodesic currents on surfaces. It
also includes several intriguing extensions of the notion of
geodesic current to various other, more general settings.
This volume features seventeen extended conference abstracts
corresponding to selected talks given by participants at the CRM
research program "Automorphisms of Free Groups: Algorithms,
Geometry and Dynamics", which took place at the Centre de Recerca
Matematica in Barcelona in fall 2012. Most of them are short
articles giving preliminary presentations of new results not yet
published in regular research journals. The articles are the result
from a direct collaboration among active researchers in the area
after working in a dynamic and productive atmosphere. The book is
intended for established researchers in the area of Group Theory,
as well as for PhD and postdoc students who wish to learn more
about the latest advances in this active area of research.
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