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Profinite Semigroups and Symbolic Dynamics

  • Book
  • © 2020

Overview

Authors:
  1. Jorge Almeida

    1. CMUP, Departamento de Matemática, Faculdade de Ciências, Universidade do Porto, Porto, Portugal

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  2. Alfredo Costa

    1. CMUC, Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade de Coimbra, Coimbra, Portugal

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  3. Revekka Kyriakoglou

    1. LIGM, Universite Gustave Eiffel, Marne La Vallee Cedex 2, France

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  4. Dominique Perrin

    1. LIGM, Universite Gustave Eiffel, Marne La Vallee Cedex 2, France

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  • The first book to describe the relation between profinite semigroups and symbolic dynamics
  • Provides new insights into both fields of profinite semigroups and symbolic dynamics
  • Defines all concepts in detail and provides numerous exercises

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2274)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    • Jorge Almeida, Alfredo Costa, Revekka Kyriakoglou, Dominique Perrin
    Pages 1-5

  3. Prelude: Profinite Integers

    • Jorge Almeida, Alfredo Costa, Revekka Kyriakoglou, Dominique Perrin
    Pages 7-23

  4. Profinite Groups and Semigroups

    • Jorge Almeida, Alfredo Costa, Revekka Kyriakoglou, Dominique Perrin
    Pages 25-85

  5. Free Profinite Monoids, Semigroups and Groups

    • Jorge Almeida, Alfredo Costa, Revekka Kyriakoglou, Dominique Perrin
    Pages 87-137

  6. Shift Spaces

    • Jorge Almeida, Alfredo Costa, Revekka Kyriakoglou, Dominique Perrin
    Pages 139-168

  7. Sturmian Sets and Tree Sets

    • Jorge Almeida, Alfredo Costa, Revekka Kyriakoglou, Dominique Perrin
    Pages 169-194

  8. The Schützenberger Group of a Minimal Set

    • Jorge Almeida, Alfredo Costa, Revekka Kyriakoglou, Dominique Perrin
    Pages 195-214

  9. Groups of Bifix Codes

    • Jorge Almeida, Alfredo Costa, Revekka Kyriakoglou, Dominique Perrin
    Pages 215-263

  10. Back Matter

    Pages 265-278
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Keywords

About this book

This book describes the relation between profinite semigroups and symbolic dynamics. Profinite semigroups are topological semigroups which are compact and residually finite. In particular, free profinite semigroups can be seen as the completion of free semigroups with respect to the profinite metric. In this metric, two words are close if one needs a morphism on a large finite monoid to distinguish them.  The main focus is on a natural correspondence between minimal shift spaces (closed shift-invariant sets of two-sided infinite words) and maximal J-classes (certain subsets of free profinite semigroups). This correspondence sheds light on many aspects of both profinite semigroups and symbolic dynamics. For example, the return words to a given word in a shift space can be related to the generators of the group of the corresponding J-class. The book is aimed at researchers and graduate students in mathematics or theoretical computer science.

Authors and Affiliations

  • CMUP, Departamento de Matemática, Faculdade de Ciências, Universidade do Porto, Porto, Portugal

    Jorge Almeida

  • CMUC, Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade de Coimbra, Coimbra, Portugal

    Alfredo Costa

  • LIGM, Universite Gustave Eiffel, Marne La Vallee Cedex 2, France

    Revekka Kyriakoglou, Dominique Perrin

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