The shift on the inverse limit of a covering projection
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.
scientific article; zbMATH DE number 4084618