The third cohomology group classifies crossed module extensions
K-Theory and Homology
2010-09-30 v2 Algebraic Topology
Group Theory
Abstract
We give an elementary proof of the well-known fact that the third cohomology group H^3(G, M) of a group G with coefficients in an abelian G-module M is in bijection to the set Ext^2(G, M) of equivalence classes of crossed module extensions of G with M.
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@article{arxiv.0911.2861,
title = {The third cohomology group classifies crossed module extensions},
author = {Sebastian Thomas},
journal= {arXiv preprint arXiv:0911.2861},
year = {2010}
}
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