The Cohomology of the Symmetric Groups

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


There are intimate connections between the homology and cohomology of the symmetric groups and algebraic topology. The first of these is their connection with the structure of cohomology operations. This arises through Steenrod’s definition of the P th power operations in terms of properties of certain elements in the groups H* (S p ; \({\Bbb F}\) P ). Indeed, the original calculation of H * (S n ; \({\Bbb F}\) P ) by Nakaoka was motivated by this connection.


Hopf Algebra Symmetric Group Weyl Group Wreath Product Regular Representation 
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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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