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The Plus Construction and Applications

  • Alejandro Adem
  • R. James Milgram
Chapter
  • 318 Downloads
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 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.

Keywords

Exact Sequence Spectral Sequence Homotopy Type Homotopy Group Poincare Series 
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 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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