Strong cocycle triviality for Z2 subshifts
نویسندگان
چکیده
منابع مشابه
Strong cocycle triviality for Z2 subshifts
We consider the cohomology of two-dimensional subshifts, and develop a new approach to proving that every cocycle is trivial (i.e. cohomologous to a homomorphism). We introduce semi-safe subshifts which, roughly speaking, have the property that some symbol can surround all allowed blocks in at least one horizontal and one vertical direction. We prove that for such subshifts, every locally const...
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The notion of topological entropy dimension for a Z-action has been introduced to measure the subexponential complexity of zero entropy systems. Given a Z2-action, along with a Z2-entropy dimension, we also consider a finer notion of directional entropy dimension arising from its subactions. The entropy dimension of a Z2-action and the directional entropy dimensions of its subactions satisfy ce...
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Kengo Matsumoto has introduced λ-graph systems and strong shift equivalence of λ-graph systems [Doc.Math.4 (1999), 285-340]. We associate to a subshift of a subshift a λ-graph system. The strong shift equivalence class of the associated λ-graph system is an invariant of subsystem equivalence. Wolfgang Krieger and Kengo Matsumoto have introduced the λ-entropy of a λ-graph system and have shown i...
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Let Ω be a Borel subset of SN where S is countable. A measure is called exchangeable on Ω, if it is supported on Ω and is invariant under every Borel automorphism of Ω which permutes at most finitely many coordinates. De-Finetti’s theorem characterizes these measures when Ω = SN. We apply the ergodic theory of equivalence relations to study the case Ω 6= SN, and obtain versions of this theorem ...
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Suppose that G is a sheaf of groups on a space X and that Uα ⊂ X is an open covering. Then a cocycle for the covering is traditionally defined to be a family of elements gαβ ∈ G(Uα ∩ Uβ) such that gαα = e and gαβgβγ = gαγ when all elements are restricted to the group G(Uα ∩ Uβ ∩ Uγ). A more compact way of saying this is to assert that such a cocycle is a map of simplicial sheaves C(U)→ BG on th...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2001
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(00)00189-4