Abstract
Let G be a finite group. As we have seen, the classifying space BG has a very simple homotopy type as it is a K(G, 1). If G is perfect then H 1 (G; ℤ) = 0; suppose that we attach cells to BG to obtain a new, but simply-connected complex BG+ with the same homology as before. Or equivalently so that the homotopy fiber of BG →BG + is acyclic, i.e. H i(F; ℤ) = 0 for all i > 0. The new complex will depend on G (as BG does) but the higher homotopy groups πi(BG+) can be highly complicated invariants of G.
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© 1994 Springer-Verlag Berlin Heidelberg
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Adem, A., Milgram, R.J. (1994). The Plus Construction and Applications. In: Cohomology of Finite Groups. Grundlehren der mathematischen Wissenschaften, vol 309. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06282-1_10
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DOI: https://doi.org/10.1007/978-3-662-06282-1_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-06284-5
Online ISBN: 978-3-662-06282-1
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