2023/08/26 by Banerjee, Arka, Okun, Boris · 1 citation
#Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2308.13965
In this paper we define the coarse (co)homology of the complement of a subspace in a metric space, generalizing the coarse (co)homology of Roe. We give a model space which encodes coarse geometric structure of the complement. We also introduce a new approach to coarse Poincaré duality spaces. We prove a version of coarse Alexander duality for these spaces and give a homological criterion for a space to be a coarse PD(n) space. Our approach is inspired by the work of Kapovich and Kleiner, but is somewhat different, and we believe, simpler.