2016/04/08 by Bell, Gregory, Moran, Danielle, Nagórko, Andrzej
#20F69 (secondary) #51K05 (primary) #54E15 #55M10 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1604.02405
The coarse category was established by Roe to distill the salient features of the large-scale approach to metric spaces and groups that was started by Gromov. In this paper, we use the language of coarse spaces to define coarse versions of asymptotic property C and decomposition complexity. We prove that coarse property C implies coarse property A; we also show that these coarse versions share many of the features of their metric analogs such as preservation by products or unions.