Duality and Its Consequences for Ordered Cohomology of Finite Type Subshifts*

نویسندگان

  • K. H. KIM
  • F. W. ROUSH
  • SUSAN G. WILLIAMS
چکیده

We construct a fundamental group for subshifts of nite type and prove that its abelianization gives a homology dual to ordered cohomology. We characterize cohomology classes representable as characteristic functions of clopen sets and give examples to illustrate what can happen for inclusions among clopen sets. We show that existence of unital ordered cohomology equivalence arising from isomorphisms of cochain groups is equivalent to homeomorphism preserving closures of orbits. We also show we can identify from the cohomology of a product of nite type subshifts, and the action of automorphisms on the rst factor, the conjugacy class of the second factor.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

FUZZY ORDERED SETS AND DUALITY FOR FINITE FUZZY DISTRIBUTIVE LATTICES

The starting point of this paper is given by Priestley’s papers, where a theory of representation of distributive lattices is presented. The purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. In this way, some results of Priestley’s papers are extended. In the main theorem, we show that the category of finite fuzzy Priestley space...

متن کامل

Existence, uniqueness and ratio decomposition for Gibbs states via duality

We give an elementary proof of existence and uniqueness of Gibbs states for Hölder weight systems on subshifts of finite type. This uses a notion of duality for such subshifts. The approach of Paterson [2] is used to construct a measure with a prescribed Jacobian and the duality is used to produce an invariant measure from this

متن کامل

Pseudovarieties Defining Classes of Sofic Subshifts Closed for Taking Shift Equivalent Subshifts

For a pseudovariety V of ordered semigroups, let S (V) be the class of sofic subshifts whose syntactic semigroup lies in V. It is proved that if V contains Sl− then S (V∗D) is closed for taking shift equivalent subshifts, and conversely, if S (V) is closed for taking conjugate subshifts then V contains LSl− and S (V) = S (V∗D). Almost finite type subshifts are characterized as the irreducible e...

متن کامل

The Basic Theorem and its Consequences

Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...

متن کامل

UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES

Let $R$ be a commutative Noetherian ring with non-zero identity and $fa$ an ideal of $R$. Let $M$ be a finite $R$--module of finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properti...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2002