Algebraic & Geometric Topology 10 (2010) 565–625

DOI: 10.2140/agt.2010.10.565

Abstract

In this paper, we determine the homotopy groups π₄(ΣK(A,1)) and π₅(ΣK(A,1)) for abelian groups A by using the following 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 π_i(ΣK(G,1)) with i = 4,5 for some nonabelian groups G = Σ₃ and SL(Z), and π₄(ΣK(A₄,1)) for the 4–th alternating group A₄.

Keywords

homotopy group, Whitehead exact sequence, spectral sequence, Moore space, suspension of K(G,1) space, simplicial group

Mathematical Subject Classification

Primary: 55Q52

Secondary: 55P20, 55P40, 55P65, 55Q35

References

Publication

Received: 26 October 2009
Accepted: 31 January 2010
Published: 7 March 2010

Authors