Pacific Journal of Mathematics

Realizing certain polynomial algebras as cohomology rings of spaces of finite type fibered over $\times B{\rm U}(d)$.

Larry Smith

Article information

Source
Pacific J. Math., Volume 126, Number 2 (1987), 361-377.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102699808

Mathematical Reviews number (MathSciNet)
MR869783

Zentralblatt MATH identifier
0656.55014

Subjects
Primary: 55R35: Classifying spaces of groups and $H$-spaces
Secondary: 55S10: Steenrod algebra

Citation

Smith, Larry. Realizing certain polynomial algebras as cohomology rings of spaces of finite type fibered over $\times B{\rm U}(d)$. Pacific J. Math. 126 (1987), no. 2, 361--377. https://projecteuclid.org/euclid.pjm/1102699808


Export citation

References

  • [I] J. Aguade and L. Smith, Modular cohomologyalgebras, Amer. J. Math., (1985), 507-530.
  • [2] N. Bourbaki, Groupes etAlgebres de Lie, Ch.4, 5, 6 Masson Paris 1981.
  • [3] W. Browder, Torsion in H-spaces, Annals of Math.,74 (1961), 24-51.
  • [4] G. Carlsson, G. B. Segas Burnside ring conjecturefor (Z/2)*, Topology, 22 (1983), 83-103.
  • [5] H. Cartan and S. Eilenberg, HomologicalAlgebra,PrincetonUniversity Press 1956.
  • [6] A. Clark and J. Ewing, The realization of polynomial algebras as cohomology rings, Pacific J. Math.,50 (1974), 425-434.
  • [7] L. E. Dickson, A fundamental system of invariants of the general modularlinear group, Trans. Amer. Math. Soc, 12 (1911), 75-98.
  • [8] W. S. Massey and F. P. Peterson, The cohomology structure of certain fibre spaces, Topology, 4 (1965), 47-65.
  • [9] W. S. Massey and F. P. Peterson, The mod 2 Cohomology Structure of Certain Fibre Spaces, Mem.Amer. Math.Soc, 74 (1967),
  • [10] H. Miller, The Sullivan Conjecture on Maps from Classifying Spaces (in Algebraic Topology Aarhus 1982 (Ed. Oliver and Madsen SLNM1051) and Univ. of Washing- ton PreprintAugust 1983).
  • [II] J. Milnor and J. C. Moore, Thestructureof Hopf algebras, Ann. of Math.,81 (1965), 211-264.
  • [12] J. P. Serre, Sur la dimension homologique des anneaux et des modules noetheriens, Tokyo Symposium 1955.
  • [13] G. D. Shephard and J. A. Todd, Finite unitary reflection groups,Canad. J. Math., 6 (1954), 274-304.
  • [14] L. Smith, Homological Algebra and the Eilenberg-Moore Spectral Sequence, Trans. Amer. Math. Soc., 129 (1967), 58-93.
  • [15] L. Smith, Hopf Fibration Towers and the Unstable Adams Spectral Sequence, Proc. Conf. Categorical Algebra, 1968.
  • [16] L. Smith, Remarks on realizing Dickson covariants as cohomology rings, Quart. J.Math. Oxford (2),36 (1985), 113-115.
  • [17] L. Smith and R. E. Stong, Chern classes, orbitpolynomials and rings of invariants, J. Algebra, (toappear).
  • [18] L. Smith and R. M. Switzer, On the realization and non-realization of Dickson algebrasas cohomology rings,Proc. Amer. Math. Soc, 89 (1983), 303-313.
  • [19] L. Smith and R. M. Switzer, Polynomial algebras over the Steenrod algebra, Proc Edinburgh Math. Soc, 27 (1984), 11-19.
  • [20] J. Tate, HomologyofNoetherian and localrings,Illinois J. Math.,(1957), 14-28.
  • [21] C. W. Wilkerson, Integral closure of unstable Steenrod algebra actions, J of P. and P. Algebra, 13 (1978), 49-55.
  • [22] A. Zabrodsky, Maps BetweenClassifying Spaces, Univ. of Jerusalem Preprint 1984.
  • [23] J. Lannes and S. Zarati, Sur les Unjectifs, Ann. Ecole. Norm. Sup. 4eme, 19 (1986), 1-31.
  • [24] L. Smith, On the invariant theory of finite pseudo reflection groups, Arch. Math., 44 (1985), 222-228.