Coarse cohomology of the complement

  • Arka Banerjee

    Auburn University, USA
  • Boris Okun

    University of Wisconsin–Milwaukee, USA
Coarse cohomology of the complement cover
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Abstract

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 space. Our approach is inspired by the work of Kapovich and Kleiner but is somewhat different, and we believe, simpler.

Cite this article

Arka Banerjee, Boris Okun, Coarse cohomology of the complement. Groups Geom. Dyn. (2025), published online first

DOI 10.4171/GGD/903