Holmstrom Classifying space

[nLab on Classifying topos and Classifying space]

Jardine-Goerss chapter V treats simplicial sets with an action of a simplicial group, classification of principal GG-fibrations, construction of a model of BGBG via universal cocycles.

There are descriptions of the mod p cohomology of the classifying spaces of compact Lie groups, see LNM1370, and Dwyer, Wilkerson: A cohomology decomposition thm (1992).

Dwyer et al: Homotopical uniqueness of classifying spaces

Book: Dwyer, Henn: Homotopy theoretic methods in group cohomology. Explains various things including nerves, equivariant homotopy theory, transfer, the T-functor of Lannes

There are results by Suslin, Jardine, Karoubi and others about bijective maps between cohomology of classifying spaces computed in topological and discrete versions. See http://www.ams.org/mathscinet-getitem?mr=764100 for some discussion about when this holds and a profinite counterexample.

For classifying spaces of algebraic groups in the setting of A1-homotopy theory, see Morel-Voevodsky: A1-homotopy theory of schemes, chapter 4. Notion of etale classifying space, and relation to algebraic K-theory.

http://mathoverflow.net/questions/51694/history-of-classifying-spaces

ALGTOP discussion here, scroll down a bit.

nLab page on Classifying space

Created on June 9, 2014 at 21:16:13 by Andreas Holmström