On homotopy groups of the suspended classifying spaces
Abstract
In this paper, we determine the homotopy groups π4( K(A,1)) and π5( 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 πi( K(G,1)) with i=4,5 for some non-abelian groups G=3 and SL(Z), and π4( K(A4,1)) for the 4-th alternating group A4.
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