On homotopy groups of the suspended classifying spaces
Algebraic Topology
2010-09-01 v2 K-Theory and Homology
Abstract
In this paper, we determine the homotopy groups \pi_4(\Sigma K(A,1)) and \pi_5(\Sigma 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 \pi_i(\Sigma K(G,1)) with i=4,5 for some non-abelian groups G=\Sigma_3 and SL(Z), and \pi_4(\Sigma K(A_4,1)) for the 4-th alternating group A_4.
Keywords
Cite
@article{arxiv.0908.3580,
title = {On homotopy groups of the suspended classifying spaces},
author = {Roman Mikhailov and Jie Wu},
journal= {arXiv preprint arXiv:0908.3580},
year = {2010}
}
Comments
Revised version, 46 pages