# 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} }

you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community…

## 31 Citations

Essential Maps Exist From BU to coker J

- Mathematics
- 1986

We show that [BU, coker J] :$ 0 but that there are no infinite loop maps from BU to coker J. The proofs involve the Segal conjecture. It is known that [coker J, BU] = 0 [HS]. A conjecture dating from…

Adams Memorial Symposium on Algebraic Topology: Progress report on the telescope conjecture

- Mathematics
- 1992

The Telescope Conjecture (made public in a lecture at Northwestern University in 1977) says that the vn–periodic homotopy of a finite complex of type n has a nice algebraic description. It also gives…

The localized slice spectral sequence, norms of Real bordism, and the Segal conjecture

- Mathematics
- 2020

In this paper, we introduce the localized slice spectral sequence, a variant of the equivariant slice spectral sequence that computes geometric fixed points equipped with residue group actions. We…

Mahowaldean families of elements in stable homotopy groups revisited

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1999

In the mid 1970s Mark Mahowald constructed a new infinite family of elements in the 2-component of the stable homotopy groups of spheres, ηj∈πSj2 (S0)(2) [M]. Using standard Adams spectral sequence…

THE POWER OF MOD P BOREL HOMOLOGY by J.P.G.Greenlees

- Mathematics
- 2006

When seeking an analogue of ordinary cohomology for spaces with a specified finite group G of symmetries we may think first of Bredon's cohomology for obstruction theory [7], and its extention to the…

The completion conjecture in equivariant cohomology

- Mathematics
- 2006

Consider RO (G)-graded an cohomology theory k G. We shall not insist on a detailed definition; suffice it to say that there is a suspension isomorphism for each real representation of G. The first…

The cyclotomic trace and algebraic K-theory of spaces

- Mathematics
- 1993

The cyclotomic trace is a map from algebraic K-theory of a group ring to a certain topological refinement of cyclic homology. The target is naturally mapped to topological Hochschild homology, and…

The Segal conjecture for topological Hochschild homology of complex cobordism

- Mathematics
- 2011

We study the Cp‐equivariant Tate construction on the topological Hochschild homology THH(B) of a symmetric ring spectrum B by relating it to a topological version R+(B) of the Singer construction,…

The smooth classification of 4-dimensional complete intersections

- Mathematics
- 2020

We prove the "Sullivan Conjecture" on the classification of 4-dimensional complete intersections up to diffeomorphism. Here an $n$-dimensional complete intersection is a smooth complex variety formed…

Topological cyclic homology of the integers

- 2019

© Société mathématique de France, 1994, tous droits réservés. L’accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l’accord avec les…

## References

SHOWING 1-10 OF 18 REFERENCES

Stable splitting of $K(G,\,1)$

- Mathematics
- 1972

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.

- Mathematics
- 1962

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

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1980

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

- MathematicsMathematical 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

- Mathematics
- 1980

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

- Mathematics
- 1974

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

New Developments in Topology: Operations of the nth kind in K-theory, and what we don't know about RP∞

- Mathematics
- 1974

Stable homotopy and generalised homology

- Mathematics
- 1974

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:…