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 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.


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

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Alejandro Adem
    • 1
  • R. James Milgram
    • 2
  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA
  2. 2.Department of Applied HomotopyStanford UniversityStanfordUSA

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