Integral cohomology of configuration spaces of the sphere

TL;DR

This paper calculates the integral and mod p cohomology of unordered configuration spaces on the sphere, providing detailed algebraic topological insights into these spaces.

Contribution

It introduces a comprehensive computation of cohomology for configuration spaces of the sphere using a cell complex approach, extending previous work with explicit calculations.

Findings

Explicit cohomology groups for configuration spaces of S^2

Comparison between integral and mod p cohomology

Application of cell complex methods to these computations

Abstract

We compute the cohomology of the unordered configuration spaces of the sphere $S^2$ with integral and with $\mathbb{Z}/p \mathbb{Z}$-coefficients using a cell complex by Fuks, Vainshtein and Napolitano.