Flow Equivalence of Shifts of Finite Type via Positive Factorizations
نویسندگان
چکیده
Together with M. Boyle and D. Huang (2000), this paper gives an alternate development of the Huang classification of shifts of finite type up to flow equivalence, and provides additional functorial information, used to analyze the action of the mapping class group of the mapping torus of a shift of finite type on the “isotopy futures” group, which is introduced here. For a shift of finite type σA, this group is isomorphic to the Bowen-Franks group cok(I−A). The action on the isotopy futures group of a subshift is the flow equivalence analogue of the dimension group representation.
منابع مشابه
Equivariant Flow Equivalence for Shifts of Finite Type, by Matrix Equivalence over Group Rings
Let G be a finite group. We classify G-equivariant flow equivalence of nontrivial irreducible shifts of finite type in terms of (i) elementary equivalence of matrices over ZG and (ii) the conjugacy class in ZG of the group of G-weights of cycles based at a fixed vertex. In the case G = Z/2, we have the classification for twistwise flow equivalence. We include some algebraic results and examples...
متن کاملOn Flow Equivalence of Sofic Shifts
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 i...
متن کاملThe Work of Kim and Roush in Symbolic Dynamics
Contents 1. Introduction 1 2. Decidability results 1 3. Shift and strong shift equivalence for Boolean matrices 3 4. Strong shift equivalence of positive matrices over subrings of R 4 5. Automorphisms of the shift 4 6. The nonzero spectra of nonnegative integral matrices 6 7. The classification problem for shifts of finite type 6 8. Classification of free Z p actions on mixing SFTs 7 9. Topolog...
متن کاملZeeman Numbers and Orbit Splitting in Flows
The Zeeman number is an invariant of flow equivalence of suspensions of shifts of finite type. We prove that the Zeeman number increases by one when splitting a periodic orbit of a Smale flow. This allows us to define the Zeeman number of any non-anomalous Anosov flow.
متن کاملOn Some New Invariants for Strong Shift Equivalence for Shifts of Finite Type
We introduce a new computable invariant for strong shift equivalence of shifts of finite type. The invariant is based on an invariant introduced by Trow, Boyle, and Marcus, but has the advantage of being readily computable. We summarize briefly a large-scale numerical experiment aimed at deciding strong shift equivalence for shifts of finite type given by irreducible 2 × 2matrices with entry su...
متن کامل