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2010 On homotopy groups of the suspended classifying spaces
Roman Mikhailov, Jie Wu
Algebr. Geom. Topol. 10(1): 565-625 (2010). 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 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.

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Roman Mikhailov. Jie Wu. "On homotopy groups of the suspended classifying spaces." Algebr. Geom. Topol. 10 (1) 565 - 625, 2010. https://doi.org/10.2140/agt.2010.10.565

Information

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

zbMATH: 1196.55017
MathSciNet: MR2602844
Digital Object Identifier: 10.2140/agt.2010.10.565

Subjects:
Primary: 55Q52
Secondary: 55P20, 55P40, 55P65, 55Q35

Rights: Copyright © 2010 Mathematical Sciences Publishers

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