Year: 2025
Type: article
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. 51Fxx; 55S91 Arka Banerjee Coarse inclusionWe adopt the notation from [12].Let .X; d / be a metric space.For A X and r 0, we define N r .A/ D fx 2 X j d.x; A/ Ä rg.We will call such neighborhoods metric neighborhoods of A. We will say that A is r-contained in B, A r B, if A N r .B/.We will say that A is coarsely contained in B, A c B, if A r B for some r 0. Two subsets are coarsely equal,
Source: Algebraic & Geometric Topology
Author: Arka Banerjee
Institution: Auburn University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4415815539