• Corpus ID: 4978456

vn-ELEMENTS IN RING SPECTRA AND APPLICATIONS TO BORDISM THEORY

@inproceedings{Hovey1997vnELEMENTSIR,
  title={vn-ELEMENTS IN RING SPECTRA AND APPLICATIONS TO BORDISM THEORY},
  author={Mark Hovey},
  year={1997}
}
The work of Hopkins and Smith [HS] has shown that the stable homotopy category has layered periodic behavior. On the (p-local) sphere, the only non-nilpotent selfmaps are multiplication by a power of p. But if we kill such a power to form the Moore space M(p), then we get a new family of non-nilpotent self maps, called the v1-self maps. Similarly, if we kill one of those, we get v2-self maps, and this behavior continues. One of the great advantages of the Brown-Peterson spectrum BP is that the… 
The power operation structure on Morava E–theory of height 2 at the prime 3
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In "Generalized Group Characters and Complex Oriented Cohomology Theories", Hopkins, Kuhn, and Ravenel develop a way to study cohomology rings of the form E^*(BG) in terms of a character map. The
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We prove that the $p$ -completed Brown–Peterson spectrum is a retract of a product of Morava $E$ -theory spectra. As a consequence, we generalize results of Kashiwabara and of Ravenel, Wilson and
THE 7-CONNECTED COBORDISM RING AT p = 3
In this paper, we study the cobordism spectrum MOh8i at the prime 3. This spectrum is important because it is conjectured to play the role for elliptic cohomology that Spin cobordism plays for real
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References

SHOWING 1-10 OF 61 REFERENCES
v1- AND V2-PERIODICITY IN STABLE HOMOTOPY THEORY
this paper we construct some self-maps related to the elements v1 E 7r2(BP) and v2 E 76(BP) and use them to obtain families in the 2-primary stable homotopy of spheres. In particular, we obtain
THE MORAVA K-THEORIES OF EILENBERG-MACLANE SPACES AND THE CONNER-FLOYD CONJECTURE
Introduction. Of the many generalized homology theories available, very few are computable in practice except for the simplest of spaces. Standard homology and K-theory are the only ones which can be
The Homotopy Type of MSU
0. Introduction. This paper examines the homotopy type of the Thom spectrum MSU associated with special unitary cobordism. For odd primes p, standard methods show that the p-localization MSU(p) is
Bousfield Localization Functors and Hopkins' Chromatic Splitting Conjecture
This paper arose from attempting to understand Bousfield localization functors in stable homotopy theory. All spectra will be p-local for a prime p throughout this paper. Recall that if E is a
Spin bordism and elliptic homology
In an attempt to understand elliptic homology at the prime 2, Ochanine Och] introduced a genus q : MSpin ! B, where B is a ring which is isomorphic to Z 1 2 ]]; ] upon inverting 2. He asked whether
A new spectrum related to 7-connected cobordism
A new 2-local spectrum Y is constructed so that H*Y is a cyclic A-module which in degrees ≤ 23 is the quotient of the Steenrod algebra by the left ideal generated by Sq1, Sq2, and Sq4. In order to
The Mod p Cohomology of BO〈4k 〉
Let B0(4k) denote the 4k -1 connected covering of BO, the classifying space for stable vector bundles. B0(4k) is the 4k-1 connected total space of a fibration 7r: B0(4k)--BO such that 7r*:
ON THE GROUPS J(X)-IV
On the Adams Spectral Sequence
  • M. Mahowald
  • Mathematics
    Canadian Journal of Mathematics
  • 1968
One of the really significant advances in stable homotopy theory has been the Adams spectral sequence (see (1) for a general discussion). To date there has been no useful general way to obtain
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5
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