2012/10/10 by Rune Johansen, Johansen, Rune
Mathematics · #37B10 (primary) #46L05 (secondary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37B10 #msc:46L05
paper · pdf · doi:10.48550/arxiv.1210.3048
143 pages, 36 figures, PhD thesis
arxiv created 2012/10/10 · openalex publication_date 2012/10/10 · arxiv updated 2012/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The flow equivalence of sofic shifts is examined using results about the structure of the corresponding covers. A canonical cover generalising the left Fischer cover to arbitrary sofic shifts is introduced and used to prove that the left Krieger cover and the past set cover of a sofic shift can be divided into natural layers. These results are used to find the range of a flow invariant and to investigate the ideal structure of the universal C^*-algebras associated to sofic shifts. The right Fischer covers of sofic beta-shifts are constructed, and it is proved that the covering maps are always 2 to 1. This is used to construct the corresponding fiber product covers and to classify these up to flow equivalence. Additionally, the flow equivalence of renewal systems is studied, and several partial results are obtained in an attempt to find the range of the Bowen-Franks invariant over the set of renewal systems of finite type. In particular, it is shown that the Bowen-Franks group is cyclic for every member of a class of renewal systems known to attain all entropies realised by shifts of finite type.