Coarse cohomology of configuration space and coarse embedding
Metric Geometry
2025-11-05 v2 Algebraic Topology
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 configuration space of a metric space and develop tools to compute this cohomology under certain conditions. As an application of this theory, we show that certain classes in the coarse cohomology of configuration space obstruct coarse embedding between two metric spaces.
Cite
@article{arxiv.2401.07720,
title = {Coarse cohomology of configuration space and coarse embedding},
author = {Arka Banerjee},
journal= {arXiv preprint arXiv:2401.07720},
year = {2025}
}
Comments
31 pages, 1 figure. Minor revisions and enhanced exposition were made in response to the referee's comments. Accepted for publication in Algebraic & Geometric Topology