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© 2017

Algorithmic and Geometric Topics Around Free Groups and Automorphisms

  • Juan González-Meneses
  • Martin Lustig
  • Enric Ventura

Benefits

  • Features a comprehensive introduction to the connections between formal language theory and group theory

  • Includes Thurston's compactification of Teichmüller space following the point of view of geodesic currents on surfaces

  • Presents specialized research topics in a friendlier way than in a research article

Textbook

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

  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

About the editors

Javier Aramayona is a Professor at the Departamento de Matemáticas of the Universidad Autónoma de Madrid, Spain.

Volker Diekert is the Head of the Theoretical Computer Science Group at the University of Stuttgart, Germany.

Christopher J. Leininger is a Professor of Mathematics at the University of Illinois at Urbana-Champaign, USA.

Pedro V. Silva is a full Professor of the Department of Mathematics of the University of Porto, Portugal.

Armin Weiβ is a Research Assistant in the Theoretical Computer Science Group at the University of Stuttgart, Germany.

Bibliographic information

  • Book Title Algorithmic and Geometric Topics Around Free Groups and Automorphisms
  • Authors Javier Aramayona
    Volker Diekert
    Christopher J. Leininger
    Pedro V. Silva
    Armin Weiß
  • Editors Juan González-Meneses
    Martin Lustig
    Enric Ventura
  • Series Title Advanced Courses in Mathematics - CRM Barcelona
  • Series Abbreviated Title Advanced Courses in Mathematics -CRM Barcelona (Birkhäuser)
  • 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 Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-319-60939-3
  • eBook ISBN 978-3-319-60940-9
  • Series ISSN 2297-0304
  • Series E-ISSN 2297-0312
  • Edition Number 1
  • Number of Pages IX, 149
  • Number of Illustrations 27 b/w illustrations, 0 illustrations in colour
  • Topics Group Theory and Generalizations
    Mathematical Applications in Computer Science
  • Buy this book on publisher's site