The Plus Construction and Applications

  • Alejandro Adem
  • R. James Milgram
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 309)


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 H1(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 BGBG + is acyclic, i. e. H i; (ℱ ℤ;) = 0 for all i > O. The new complex will depend on G (as BG does) but the higher homotopy groups π i(BG +) can be highly complicated invariants of G.


Spectral Sequence Homotopy Type Homotopy Group Poincare Series Homotopy Fiber 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Alejandro Adem
    • 1
  • R. James Milgram
    • 2
  1. 1.Department of Mathematics, Van Vleck HallUniversity of WisconsinMadisonUSA
  2. 2.Department of MathematicsStanford UniversityStanfordUSA

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