On the second cohomology group of a simplicial group

Details On the second cohomology group of a simplicial group On the second cohomology group of a simplicial group

2009-11-15

arxiv.org/abs/0911.2864v2

Homology, Homotopy and Applications 12(2) (2010), pp. 167-210

Mathematics

Algebraic Topology

Further references added. This article is an extension of the published version

Scientific paper

We give an algebraic proof for the result of Eilenberg and Mac Lane that the
second cohomology group of a simplicial group G can be computed as a quotient
of a fibre product involving the first two homotopy groups and the first
Postnikov invariant of G. Our main tool is the theory of crossed module
extensions of groups.

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