# 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…

## 23 Citations

The power operation structure on Morava E–theory of height 2 at the prime 3

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Given a maximal finite subgroup G of the nth Morava stabilizer group at a prime p, we address the question: is the associated higher real K‐theory EOn a summand of the K(n)‐localization of a TAF…

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We recall the study of MU [2k,∞)–orientations as elucidated by Ando, Hopkins, and Strickland. Their work prompts us to investigate a particular algebraic moduli which, after 2–localization, we…

Transchromatic generalized character maps

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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…

Invertible Spectra in the E(n)‐Local Stable Homotopy Category

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Suppose C is a category with a symmetric monoidal structure, which we will refer to as the smash product. Then the Picard category is the full subcategory of objects which have an inverse under the…

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The generalized character map of Hopkins, Kuhn, and Ravenel [9] can be interpreted as a map of cohomology theories beginning with a height n cohomology theory E and landing in a height 0 cohomology…

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- MathematicsCompositio Mathematica
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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

- Mathematics
- 1995

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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