Homology, Homotopy and Applications

Volume 12 (2010)

Number 2

On the second cohomology group of a simplicial group

Pages: 167 – 210

DOI: http://dx.doi.org/10.4310/HHA.2010.v12.n2.a6

Author

Sebastian Thomas (Lehrstuhl D für Mathematik, RWTH Aachen University, Aachen, Germany)

Abstract

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.

Keywords

cohomology; simplicial groups; crossed modules

2010 Mathematics Subject Classification

18D35, 18G30, 20J06, 55U10

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