Skip to main content
SpringerLink
Log in

Constructing modular classifying spaces

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

Using the homotopy limit construction over a certain small category, we construct spaces whose modp cohomology algebras are the rings of invariants of some unitary reflection groups of order divisible byp.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

References

  1. J. F. Adams and C. Wilkerson,Finite H-spaces and algebras over the Steenrod algebra, Ann. Math.111 (1980), 95–143.

    Article  MathSciNet  Google Scholar 

  2. J. Aguadé,Computing Lannes T functor, preprint, 1987.

  3. J. Aguadé,Constructing modular classifying spaces II, in preparation.

  4. G. Bagnera,I gruppi finiti di transformazioni lineari dello spazio che contengono omologie, Rend. Circ. Mat. Palermo19 (1905), 1–56.

    Article  MATH  Google Scholar 

  5. M. Benard,Schur indices and splitting fields of the unitary reflection groups, J. Algebra38 (1976), 318–342.

    Article  MATH  MathSciNet  Google Scholar 

  6. M. Benard,Characters and Schur indices of the unitary reflection group [321]3, Pacific J. Math.58 (1975), 309–321.

    MATH  MathSciNet  Google Scholar 

  7. H. F. Blichfeldt,The finite discontinuous primitive groups of collineations in four variables, Math. Ann.60 (1905), 204–231.

    Article  MathSciNet  MATH  Google Scholar 

  8. A. K. Bousfield and D. M. Kan,Homotopy Limits, Completions and Localizations, Lecture Notes in Math.304, Springer-Verlag, Berlin, 1972.

    MATH  Google Scholar 

  9. A. Clark and J. Ewing,The realization of polynomial algebras as cohomology rings, Pacific J. Math.50 (1974), 425–434.

    MATH  MathSciNet  Google Scholar 

  10. A. Cohen,Finite complex reflection groups, Ann. Sci. Éc. Norm. Sup.9 (1976), 379–436.

    MATH  Google Scholar 

  11. J. H. Conwayet al., Atlas of Finite Groups, Clarendon Press, Oxford, 1985.

    MATH  Google Scholar 

  12. W. Dwyer, H. Miller and C. Wilkerson,Uniqueness of classifying spaces, mimeographed notes, 1986.

  13. C. M. Hamill,On a finite group of order 6,531,840, Proc. London Math. Soc.3 (1953), 401–454.

    Article  MathSciNet  Google Scholar 

  14. C. M. Hamill,A collineation group of order 21335527, London Math. Soc.3 (1953), 54–79.

    Article  MATH  MathSciNet  Google Scholar 

  15. S. Jackowski and J. E. McClure,Homotopy approximations for classifying spaces of compact Lie groups, Proc. of the Arcata Conference, 1986, to appear.

  16. F. Klein,Über eine geometrische Repräsentation der Resolventen algebraischer Gleichungen, Math. Ann.4 (1871).

  17. H. Maschke,Über die quaternäre, endliche, lineare substitutionsgruppe der Borchardt’schen Moduln, Math. Ann.30 (1887), 496–515.

    Article  MathSciNet  Google Scholar 

  18. D. Quillen,On the cohomology and K-theory of the general linear group over a finite field, Ann. Math.96 (1972), 552–586.

    Article  MathSciNet  Google Scholar 

  19. G. C. Shephard,Unitary groups generated by reflections, Can. J. Math.5 (1953), 364–383.

    MATH  MathSciNet  Google Scholar 

  20. G. C. Shephard,Abstract definitions for reflection groups, Can. J. Math.9 (1957), 273–276.

    MATH  MathSciNet  Google Scholar 

  21. G. C. Shephard and J. A. Todd,Finite unitary reflection groups, Can. J. Math.6 (1954), 274–304.

    MATH  MathSciNet  Google Scholar 

  22. L. Smith,Realizability and nonrealizability of Dickson algebras as cohomology rings, Proc. Am. Math. Soc.89 (1983), 303–313.

    Article  MATH  Google Scholar 

  23. A. Zabrodsky,On the realization of invariant subgroups ofπ*X, Trans. Am. Math. Soc.285 (1984), 467–496.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain

    J. Aguadé

Authors
  1. J. Aguadé
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aguadé, J. Constructing modular classifying spaces. Israel J. Math. 66, 23–40 (1989). https://doi.org/10.1007/BF02765884

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02765884

Keywords

Search

Navigation