Algorithmic and Geometric Topics Around Free Groups and Automorphisms

  • Javier Aramayona
  • Volker Diekert
  • Christopher J. Leininger
  • Pedro V. Silva
  • Armin Weiß
  • Juan González-Meneses
  • Martin Lustig
  • Enric Ventura

Part of the Advanced Courses in Mathematics - CRM Barcelona book series (ACMBIRK)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Volker Diekert, Armin Weiß
    Pages 43-110
  3. Javier Aramayona, Christopher J. Leininger
    Pages 111-149

About this book

Introduction

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 Matemàtica (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 Teichmüller 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.

Keywords

languages automata virtually-free groups endomorphisms Bass-Serre treewidth hyperbolicity Teichmüller space compactification geodesic current

Authors and affiliations

  • Javier Aramayona
    • 1
  • Volker Diekert
    • 2
  • Christopher J. Leininger
    • 3
  • Pedro V. Silva
    • 4
  • Armin Weiß
    • 5
  1. 1.Universidad Autónoma de Madrid - ICMATMadridSpain
  2. 2.Institut für Formale Methoden der InformatikUniversität StuttgartStuttgartGermany
  3. 3.Department of MathematicsUniversity of Illinois Urbana-ChampaignUrbanaUSA
  4. 4.Centro de MatemáticaUniversidade do PortoPortoPortugal
  5. 5.Institut für Formale Methoden der InformatikUniversität StuttgartStuttgartGermany

Editors and affiliations

  • Juan González-Meneses
    • 1
  • Martin Lustig
    • 2
  • Enric Ventura
    • 3
  1. 1.Universidad de SevillaFacultad de Matemáticas Universidad de SevillaSevillaSpain
  2. 2.Centre de Mathématiques et InformatiqueUniversité Aix-Marseille III Centre de Mathématiques et InformatiqueMarseilleFrance
  3. 3.Departament de MatemàtiquesUniversitat Politècnica de Cataluny Departament de MatemàtiquesBarcelonaSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-60940-9
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-60939-3
  • Online ISBN 978-3-319-60940-9
  • Series Print ISSN 2297-0304
  • Series Online ISSN 2297-0312
  • About this book