The shift on the inverse limit of a covering projection
type: Item
instance of: scholarly article
title: The shift on the inverse limit of a covering projection
zbMATH Open document ID: 0663.58031
DOI: 10.1007/BF02787257
author: Cem Tezer
published in: Israel Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The notion of shift equivalence was introduced by \textit{R. F. Williams} and used in his analysis of expanding attractors [Global analysis, Proc. Symp. Pure Math. 14, 341-361 (1970; Zbl 0213.504); Ann. Math., II. Ser. 98, 120-153 (1973); Errata ibid. 99, 380-381 (1974; Zbl 0282.58008); Inst. Haut. Etud. Sci. Publ. Math. 43(1973), 169-203 (1974; Zbl 0279.58013)]. In the present paper several theorems are proved. The precise statements of the typical results are somewhat technical but the main results are the following: if two shifts defined on the inverse limit spaces of two covering projections are topologically conjugate then the maps induced by the projections on the fundamental groups of the covering spaces are (weakly) shift equivalent and for expanding endomorphisms of compact manifolds weak shift equivalence is a complete invariant of topological conjugacy. As an application of the second result a classification is given for all shifts of expanding maps defined on the Klein bottle.
Mathematics Subject Classification ID: 37-XX
zbMATH DE Number: 4084618
zbMATH Keywords: topological conjugacy
zbMATH Keywords: shift equivalence
reviewed by: C. Chicone
MaRDI profile type: Publication
cites work: Q5608683
cites work: Anosov endomorphisms
cites work: Endomorphisms of Compact Differentiable Manifolds
cites work: Classification of subshifts of finite type
cites work: Q5615935
cites work: Expanding attractors
description: scientific article; zbMATH DE number 4084618