nLab cohomology of classifying spaces

Ordinary cohomology

Computed by Borel in 1950s: 1, 2.

Differential cohomology


  • Armand Borel, Sur La Cohomologie des Espaces Fibres Principaux et des Espaces Homogenes de Groupes de Lie Compacts, Annals of Mathematics 57:1 (1953), 115.

  • Armand Borel, Sur L’Homologie et la Cohomologie des Groupes de Lie Compacts Connexes, American Journal of Mathematics 76:2 (1954), 273.

Integral coefficients:

  • Edgar H. Brown, The cohomology of BSO nBSO_n and BO nBO_n with integer coefficients, Proceedings of the American Mathematical Society 85:2, 283-288. doi.

  • Mark Feshbach?, The Integral Cohomology Rings of the Classifying Spaces of O(n) and SO(n), Indiana Univ. Math. J. 32 No. 4 (1983), 511–516. doi.

  • Feifei Fan, The cohomology of the classifying space of PU(4)PU(4), arXiv.

Differential cohomology:

  • Ivan Kolář, Gauge-Natural Forms of Chern-Weil Type, Annals of Global Analysis and Geometry 11: 41–47, 1993.

Last revised on May 16, 2024 at 17:30:06. See the history of this page for a list of all contributions to it.