Homology, Homotopy and Applications

Volume 21 (2019)

Number 1

Integral cohomology of configuration spaces of the sphere

Pages: 283 – 302

DOI: https://dx.doi.org/10.4310/HHA.2019.v21.n1.a13


Christoph Schiessl (ETH Zurich, Steinmaur, Switzerland)


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 due to Fox, Neuwirth, Fuks, Vainshtein and Napolitano.


homology, configuration space

2010 Mathematics Subject Classification


The author was supported by the grant ERC-2012-AdG-320368-MCSK.

This is part of the author’s PhD thesis.

Copyright © 2018, Christoph Schiessl. Permission to copy for private use granted.

Received 22 January 2018

Received revised 16 July 2018

Published 17 October 2018