Homology, Homotopy and Applications

Volume 21 (2019)

Number 1

Integral cohomology of configuration spaces of the sphere

Pages: 283 – 302

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

Author

Christoph Schiessl (ETH Zurich, Steinmaur, Switzerland)

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

Keywords

homology, configuration space

2010 Mathematics Subject Classification

55R80

Full Text (PDF format)

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