Profinite Semigroups and Symbolic Dynamics

by Jorge Almeida, Alfredo Costa, Revekka Kyriakoglou, Dominique Perrin

Overview

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.

Product Details

ISBN-13:	9783030552152
Publisher:	Springer-Verlag New York, LLC
Publication date:	09/10/2020
Series:	Lecture Notes in Mathematics , #2274
Sold by:	Barnes & Noble
Format:	eBook
File size:	14 MB
Note:	This product may take a few minutes to download.

Table of Contents

- 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.