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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The $ 7$-connected cobordism ring at $ p=3$


Authors: Mark A. Hovey and Douglas C. Ravenel
Journal: Trans. Amer. Math. Soc. 347 (1995), 3473-3502
MSC: Primary 55N22; Secondary 55P42, 55T15
MathSciNet review: 1297530
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Abstract: In this paper, we study the cobordism spectrum $ MO\left\langle 8 \right\rangle $ 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 $ K$-theory. We show that the torsion is all killed by $ 3$, and that the Adams-Novikov spectral sequence collapses after only $ 2$ differentials. Many of our methods apply more generally.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1297530-2
PII: S 0002-9947(1995)1297530-2
Article copyright: © Copyright 1995 American Mathematical Society