Coarse cohomology of configuration space and coarse embedding

Banerjee, Arka

doi:10.2140/agt.2025.25.4391

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Coarse cohomology of configuration space and coarse embedding

Arka Banerjee

Algebraic & Geometric Topology 25 (2025) 4391–4426

DOI: 10.2140/agt.2025.25.4391

Abstract

We introduce a notion of equivariant coarse cohomology of the complement of a subspace in a metric space. We use this cohomology to define a notion of coarse cohomology of the two-points configuration space of a metric space and develop tools to compute this cohomology under various conditions. As an application of this theory, we show that certain classes in the coarse cohomology of two-points configuration space obstruct coarse embedding between two metric spaces.

Keywords

configuration space, coarse cohomology, coarse embedding

Mathematical Subject Classification

Primary: 51Fxx

Secondary: 55S91

References

Publication

Received: 18 May 2024

Revised: 24 September 2024

Accepted: 2 November 2024

Published: 29 October 2025

Authors

Arka Banerjee
Department of Mathematics and Statistics Auburn University Auburn, AL United States

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Volume 25, issue 7 (2025)