Coarse cohomology of the complement

Arka Banerjee; Boris Okun

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arXiv · 2308.13965

Coarse cohomology of the complement

Arka Banerjee·Boris Okun

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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 Poincar\'e 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.

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Arka Banerjee, Boris Okun. 2023-08-26. Coarse cohomology of the complement. https://arxiv.org/abs/2308.13965

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