The Cuntz semigroup of some spaces of dimension at most 2

Details The Cuntz semigroup of some spaces of dimension at most 2 The Cuntz semigroup of some spaces of dimension at most 2

2007-11-28

arxiv.org/abs/0711.4396v4

Mathematics

Operator Algebras

Scientific paper

The Cuntz semigroup is computed for spaces $X$ of dimension at most 2 such that $\check H^2(X,\Z)=0$. This computation is then extended to spaces of dimension at most 2 such that $\check H^2(X\backslash\{x\},\Z)=0$ for all $x\in X$ (e.g., any compact surface). It is also shown that for these two classes of spaces the Cuntz equivalence of countably generated Hilbert C*-modules (over $C_0(X)$) amounts to their isomorphism.

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