Cohomology of generalised configuration spaces of points on ℝ^r

2020/04/17 by Marcel Bökstedt, Bökstedt, Marcel, Erica Minuz +1
Computer Science · Mathematics · #55N99 #55R80 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2004.08370

openalex publication_date 2020/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the cohomology ring of a generalised type of configuration space of points in ℝ^r. This configuration space is indexed by a graph. In the case the graph is complete the result is known and it is due to Arnold and Cohen. However, our computations give a generalisation to any graph and an alternative proof of the classical result. Moreover, we show that there are deletion-contraction short exact sequences for this cohomology rings.

Citations

• On configuration spaces, their homology, and Lie algebras

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• The cohomology ring away from 2 of configuration spaces on real projective spaces
• Graph cohomologies and rational homotopy type of configuration spaces
• Configuration spaces in algebraic topology
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