Integral cohomology of configuration spaces of the sphere

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.

Keywords

homology, configuration space

2010 Mathematics Subject Classification

55R80

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

This is part of the author’s PhD thesis.

Received 22 January 2018

Received revised 16 July 2018

Published 17 October 2018