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On the cohomology of configuration spaces

  • Erich Ossa
Conference paper
Part of the Progress in Mathematics book series (PM, volume 136)

Abstract

The aim of this note is to show how previous combinatorial calculations in the computation of the cohomology of configuration spaces can be considerably simplified by more conceptual arguments involving some representation theory. Since I first lectured on these results some other accounts have been given ([CT93, Str93]), partly overlapping with this. Nevertheless. it seemed still worthwhile to publish a full account of these considerations.

Keywords

Symmetric Group Spectral Sequence Configuration Space Braid Group Trivial Representation 
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References

  1. [Arn69]
    V. Arnold: The Cohomology Ring of the Colored Braid Groups, Edinburgh Math. Notes 5 (1969), 138–140Google Scholar
  2. [BV68]
    J. M. Boardman, R. Vogt: Homotopy-everything H-spaces, Bull. AMS 74 (1968), 1117–1122MathSciNetzbMATHCrossRefGoogle Scholar
  3. [CLM76]
    F. R. Cohen, T. Lada, J. P. May: The homology of iterated loop spaces, Lecture Notes in Math. 533 (1976)zbMATHGoogle Scholar
  4. [Coh85]
    F. R. Cohen: Artin’s braid groups and classical homotopy theory, Contemp. Math. 44 (1985), 207–220Google Scholar
  5. [Coh88]
    F. R. Cohen: Artirís braid groups, classical homotopy theory, and sundry other curiosities, Contemp. Math. 78 (1988), 167–206Google Scholar
  6. [CMT78]
    F. R. Cohen, J. P. May, L. R. Taylor: Splitting of certain spaces CX, Proc. Camb. Phil. Soc. 84 (1978), 465–496MathSciNetzbMATHCrossRefGoogle Scholar
  7. [CT78]
    F. R. Cohen, L. Taylor: Computations of Gelfand-Fuks cohomology, the cohomology of function spaces and the cohomology of configuration spaces, Lecture Notes in Math. 657 (1978), 106–143Google Scholar
  8. [CT93]
    F. R. Cohen, L. Taylor: On the representation theory associated to the cohomology of configuration spaces, Contemp. Math. 146 (1993), 167–206MathSciNetGoogle Scholar
  9. [FN62]
    E. Fadell, L. Neuwirth: Configuration spaces, Math. Scand. 10 (1962), 119–126MathSciNetGoogle Scholar
  10. [Fuk70]
    D. B. Fuks: Cohomologies of the group cos mod 2, Functional Analysis Appl. 4 (1970), 143–151zbMATHCrossRefGoogle Scholar
  11. [Leh86]
    G. I. Lehrer: On the action of the symmetric group on the cohomology of the complement of its reflecting hyperplanes, J. Algebra 104 (1986), 410–424MathSciNetzbMATHCrossRefGoogle Scholar
  12. [Leh87]
    G. I. Lehrer: On the Poincaré series associated with Coxeter group actions on complements of hyperplanes, J. Lond. Math. Soc. 36 (1987), 275–294MathSciNetzbMATHCrossRefGoogle Scholar
  13. [Leh88]
    G. I. Lehrer: A survey of Hecke algebras and the Artin braid groups, Contemp. Math. 78 (1988), 365–383MathSciNetGoogle Scholar
  14. [May72]
    J. P. May: The geometry of iterated loop spaces, Springer Lecture Notes 271 (1972)zbMATHGoogle Scholar
  15. [Rog93]
    J. Rognes: The rank filtration in algebraic K-theory, Topology 31 (1993), 813–845MathSciNetCrossRefGoogle Scholar
  16. [Seg73]
    G. Segal: Configuration spaces and iterated loop spaces, Invent. Math. 21 (1973), 213–221MathSciNetzbMATHCrossRefGoogle Scholar
  17. [Str93]
    N. P. Strickland: Geometry and topology of configuration spaces, Preprint MIT 1993Google Scholar

Copyright information

© Birkhäuser Verlag 1996

Authors and Affiliations

  • Erich Ossa
    • 1
  1. 1.Fachbereich 7 - MathematikBergische Universität, Gesamthochschule WuppertalWuppertalGermany

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