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The Plus Construction and Applications

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

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 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.

Keywords

Spectral Sequence Homotopy Type Homotopy Group Poincare Series Homotopy Fiber 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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