The Segal Conjecture for Cyclic Groups and its Consequences

@article{Ravenel1984TheSC,
  title={The Segal Conjecture for Cyclic Groups and its Consequences},
  author={Douglas C. Ravenel},
  journal={American Journal of Mathematics},
  year={1984},
  volume={106},
  pages={415}
}
  • D. Ravenel
  • Published 1 April 1984
  • History
  • American Journal of Mathematics
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References

SHOWING 1-10 OF 18 REFERENCES
Stable splitting of $K(G,\,1)$
the splitting of the cohomology (ordinary and generalized) of K(G, 1), for finite abelian G, is realized topologically by taking suspensions. The cohomology of K(ZF,, 1), both ordinary and
On axiomatic homology theory.
provide a protective representation of H(X) as a direct product. It is easily verified that the singular homology and cohomology theories are additive. Also the Cech theories based on infinite
Calculation of Lin's Ext groups
The first-named author has proved interesting results about the stable homotopy and cohomotopy of spaces related to real projective space RP∞; these are presented in an accompanying paper (6). His
The Kahn–Priddy theorem
  • J. Adams
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1973
Let ΦSr(X) be the stable homotopy group where SnX means the n-fold suspension of X. For example, the groups ΦSr(S0) are the stable homotopy groups of spheres. Let be the ‘infinite-dimensional’
On conjectures of Mahowald, Segal and Sullivan
In this paper we prove some results about the stable homotopy and cohomotopy of spaces related to the infinite real protective space RP∞. These include M. E. Mahowald's conjecture on the limit of
Equivariant function spaces and stable homotopy theory I
Nutzungsbedingungen Mit dem Zugriff auf den vorliegenden Inhalt gelten die Nutzungsbedingungen als akzeptiert. Die angebotenen Dokumente stehen für nicht-kommerzielle Zwecke in Lehre, Forschung und
On conjectures of Mahowald
  • Segal and Sullivan, Math. Proc. Camb. Phil. Soc. 87
  • 1980
Stable homotopy and generalised homology
Preface Pt. I: S.P. Novikov's Work on Operations on Complex Cobordism 2: Cobordism groups 3: Homology 4: The Conner-Floyd Chern classes 5: The Novikov operations 6: The algebra of all operations 7:
...
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