Almeida / Costa / Kyriakoglou Profinite Semigroups and Symbolic Dynamics

1. Auflage 2020
ISBN: 978-3-030-55215-2
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 2274, 278 Seiten, eBook

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Almeida, Jorge

Costa, Alfredo

Kyriakoglou, Revekka

Perrin, Dominique

Inhaltsverzeichnis

- Introduction. - Prelude: Profinite Integers. - Profinite Groups and Semigroups. - Free Profinite Monoids, Semigroups and Groups. - Shift Spaces. - Sturmian Sets and Tree Sets. - The Schützenberger Group of a Minimal Set. - Groups of Bifix Codes.