Asymptotic dimension, Property A, and Lipschitz maps

Details Asymptotic dimension, Property A, and Lipschitz maps Asymptotic dimension, Property A, and Lipschitz maps

2009-09-22

arxiv.org/abs/0909.4095v1

Mathematics

Metric Geometry

10 pages

Scientific paper

It is well-known that a paracompact space X is of covering dimension n if and only if any map f from X to a simplicial complex K can be pushed into its n-skeleton. We use the same idea to define dimension in the coarse category. It turns out the analog of maps f from X to K is related to asymptotically Lipschitz maps, the analog of paracompact spaces are spaces related to Yu's Property A, and the dimension coincides with Gromov's asymptotic dimension.

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