Cohomological Approach to Asymptotic Dimension
نویسندگان
چکیده
We introduce the notion of asymptotic cohomology based on the bounded cohomology and define cohomological asymptotic dimension asdimZ X of metric spaces. We show that it agrees with the asymptotic dimension asdimX when the later is finite. Then we use this fact to construct an example of a metric space X of bounded geometry with finite asymptotic dimension for which asdim(X × R) = asdimX. In particular, it follows for this example that the coarse asymptotic dimension defined by means of Roe’s coarse cohomology is strictly less than its asymptotic dimension.
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