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- W4298266362 abstract "Given a factor map $p : (X,T) to (Y,S)$ of Cantor minimal systems, we study the relations between the dimension groups of the two systems. First, we interpret the torsion subgroup of the quotient of the dimension groups $K_0(X)/K_0(Y)$ in terms of intermediate extensions which are extensions of $(Y,S)$ by a compact abelian group. Then we show that, by contrast, the existence of an intermediate non-abelian finite group extension can produce a situation where the dimension group of $(Y,S)$ embeds into a proper subgroup of the dimension group of $(X,T)$, yet the quotient of the dimension groups is nonetheless torsion free. Next we define higher order cohomology groups $H^n(X mid Y)$ associated to an extension, and study them in various cases (proximal extensions, extensions by, not necessarily abelian, finite groups, etc.). Our main result here is that all the cohomology groups $H^n(X mid Y)$ are torsion groups. As a consequence we can now identify $H^0(X mid Y)$ as the torsion group of $ K_0(X)/K_0(Y)$." @default.
- W4298266362 created "2022-10-01" @default.
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- W4298266362 date "2013-01-01" @default.
- W4298266362 modified "2023-09-25" @default.
- W4298266362 title "Extensions of Cantor minimal systems and dimension groups." @default.
- W4298266362 hasPublicationYear "2013" @default.
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