On homotopy groups of the suspended classifying spaces

Details On homotopy groups of the suspended classifying spaces On homotopy groups of the suspended classifying spaces

2009-08-25

arxiv.org/abs/0908.3580v2

Alg. Geom. Top. 10 (2010), 565-625

Mathematics

Algebraic Topology

Revised version, 46 pages

Scientific paper

In this paper, we determine the homotopy groups \pi_4(\Sigma K(A,1)) and \pi_5(\Sigma K(A,1)) for abelian groups A by using different facts and methods from group theory and homotopy theory: derived functors, the Carlsson simplicial construction, the Baues-Goerss spectral sequence, homotopy decompositions and the methods of algebraic K-theory. As the applications, we also determine \pi_i(\Sigma K(G,1)) with i=4,5 for some non-abelian groups G=\Sigma_3 and SL(Z), and \pi_4(\Sigma K(A_4,1)) for the 4-th alternating group A_4.

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