Asymptotic dimension, property A, and Lipschitz maps
Copyright policy )Asymptotic dimension, property A, and Lipschitz maps
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.
10 pages
- University of Tennessee at Knoxville United States
- University of Ljubljana Slovenia
54F45, 55M10, Mathematics - Geometric Topology, Mathematics - Metric Geometry, FOS: Mathematics, Metric Geometry (math.MG), Geometric Topology (math.GT)
54F45, 55M10, Mathematics - Geometric Topology, Mathematics - Metric Geometry, FOS: Mathematics, Metric Geometry (math.MG), Geometric Topology (math.GT)
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).7 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!