Volume 10, issue 1 (2010)

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On homotopy groups of the suspended classifying spaces

Roman Mikhailov and Jie Wu

Algebraic & Geometric Topology 10 (2010) 565–625
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 πi(ΣK(G,1)) with i = 4,5 for some nonabelian groups G = Σ3 and SL(), 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 2000
Primary: 55Q52
Secondary: 55P20, 55P40, 55P65, 55Q35
References
Publication
Received: 26 October 2009
Accepted: 31 January 2010
Published: 7 March 2010
Authors
Roman Mikhailov
Steklov Mathematical Institute
Gubkina 8
Moscow 119991
Russia
Jie Wu
Department of Mathematics
National University of Singapore
2Block S17 (SOC1), 06-02
10 Lower Kent Ridge Road
Singapore 119076
Singapore
http://www.math.nus.edu.sg/~matwujie