## Algebraic & Geometric Topology

### On homotopy groups of the suspended classifying spaces

#### 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 $SL(ℤ)$, and $π4(ΣK(A4,1))$ for the $4$–th alternating group $A4$.

#### Article information

Source
Algebr. Geom. Topol., Volume 10, Number 1 (2010), 565-625.

Dates
Received: 26 October 2009
Accepted: 31 January 2010
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513882323

Digital Object Identifier
doi:10.2140/agt.2010.10.565

Mathematical Reviews number (MathSciNet)
MR2602844

Zentralblatt MATH identifier
1196.55017

#### Citation

Mikhailov, Roman; Wu, Jie. On homotopy groups of the suspended classifying spaces. Algebr. Geom. Topol. 10 (2010), no. 1, 565--625. doi:10.2140/agt.2010.10.565. https://projecteuclid.org/euclid.agt/1513882323

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