Cohomological approach to asymptotic dimension |
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Authors: | A Dranishnikov |
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Institution: | (1) Department of Mathematics, University of Florida, P.O. Box 118105, 358 Little Hall, Gainesville, FL 32611-8105, USA |
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Abstract: | We introduce the notion of asymptotic cohomology based on the bounded cohomology and define cohomological asymptotic dimension
asdim
Z
X of metric spaces. We show that it agrees with the asymptotic dimension asdim X 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) = asdim X. 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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Keywords: | Asymptotic dimension Bounded cohomology Coarse cohomology Asymptotic cohomological dimension Coarse cohomological dimension |
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