scholarly journals Flow equivalence of shifts of finite type via positive factorizations

2002 ◽  
Vol 204 (2) ◽  
pp. 273-317 ◽  
Author(s):  
Mike Boyle
Keyword(s):  
Finite Type ◽  
Flow Equivalence

Flow equivalence of subshifts of finite type

1984 ◽  
Vol 4 (1) ◽  
pp. 53-66 ◽  
Author(s):  
John Franks
Keyword(s):  
Finite Type ◽  
Suspension Flows ◽  
Flow Equivalence ◽  
Complete Set ◽  
Subshifts Of Finite Type

AbstractA complete set of computable invariants is given for deciding whether two irreducible subshifts of finite type have topologically equivalent suspension flows.

Flow equivalence of reducible shifts of finite type

1994 ◽  
Vol 14 (4) ◽  
pp. 695-720 ◽  
Author(s):  
Danrung Huang
Keyword(s):  
Finite Type ◽  
Irreducible Components ◽  
Flow Equivalence

AbstractUsing an invariant of Cuntz, we classify reducible shifts of finite type with two irreducible components up to flow equivalence.

scholarly journals Flow equivalence of sofic beta-shifts

2016 ◽  
Vol 37 (3) ◽  
pp. 786-801 ◽  
Author(s):  
RUNE JOHANSEN
Keyword(s):  
Finite Type ◽  
Classification Problem ◽  
Flow Classification ◽  
Fiber Product ◽  
Sofic Shifts ◽  
Flow Equivalence

The Fischer, Krieger, and fiber product covers of sofic beta-shifts are constructed and used to show that every strictly sofic beta-shift is 2-sofic. Flow invariants based on the covers are computed, and shown to depend only on a single integer that can easily be determined from the $\unicode[STIX]{x1D6FD}$-expansion of 1. It is shown that any beta-shift is flow equivalent to a beta-shift given by some $1<\unicode[STIX]{x1D6FD}<2$, and concrete constructions lead to further reductions of the flow classification problem. For each sofic beta-shift, there is an action of $\mathbb{Z}/2\mathbb{Z}$ on the edge shift given by the fiber product, and it is shown precisely when there exists a flow equivalence respecting these $\mathbb{Z}/2\mathbb{Z}$-actions. This opens a connection to ongoing efforts to classify general irreducible 2-sofic shifts via flow equivalences of reducible shifts of finite type (SFTs) equipped with $\mathbb{Z}/2\mathbb{Z}$-actions.

scholarly journals Flow equivalence and orbit equivalence for shifts of finite type and isomorphism of their groupoids

2019 ◽  
Vol 469 (2) ◽  
pp. 1088-1110 ◽  
Author(s):  
Toke Meier Carlsen ◽  
Søren Eilers ◽  
Eduard Ortega ◽  
Gunnar Restorff
Keyword(s):  
Finite Type ◽  
Orbit Equivalence ◽  
Flow Equivalence

A stochastic analogue of a theorem of Boyle's on almost flow equivalence

1993 ◽  
Vol 13 (3) ◽  
pp. 417-444 ◽  
Author(s):  
Paulo Ventura Araújo
Keyword(s):  
Finite Type ◽  
Topological Classification ◽  
Suspension Flows ◽  
Axiom A ◽  
Stochastic Version ◽  
Flow Equivalence ◽  
Subshifts Of Finite Type ◽  
Basic Sets

AbstractWe study a new topological classification of suspension flows on subshifts of finite type, and obtain a new proof of a theorem of Boyle's which states that, in an appropriate sense, all such flows are alike. We prove that the stochastic version of this classification is non-trivial by exhibiting a certain invariant, and show that this invariant is complete in a particular case, although not in general. Symbolic flows are important as models of basic sets of Axiom A flows, and so we discuss the significance of our results for this latter type of flow.

ON FINITE TYPE 3-MANIFOLD INVARIANTS I

1996 ◽  
Vol 05 (04) ◽  
pp. 441-461 ◽  
Author(s):  
STAVROS GAROUFALIDIS
Keyword(s):  
Vector Space ◽  
Finite Type ◽  
Commutative Algebra ◽  
Integral Homology ◽  
Knot Invariants ◽  
Finite Type Invariants ◽  
Definition Of ◽  
Type 3

Recently Ohtsuki [Oh2], motivated by the notion of finite type knot invariants, introduced the notion of finite type invariants for oriented, integral homology 3-spheres. In the present paper we propose another definition of finite type invariants of integral homology 3-spheres and give equivalent reformulations of our notion. We show that our invariants form a filtered commutative algebra. We compare the two induced filtrations on the vector space on the set of integral homology 3-spheres. As an observation, we discover a new set of restrictions that finite type invariants in the sense of Ohtsuki satisfy and give a set of axioms that characterize the Casson invariant. Finally, we pose a set of questions relating the finite type 3-manifold invariants with the (Vassiliev) knot invariants.

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