The 7-connected cobordism ring at 𝑝=3

Hovey, Mark A.; Ravenel, Douglas C.

doi:10.1090/S0002-9947-1995-1297530-2

The $7$-connected cobordism ring at $p=3$
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by Mark A. Hovey and Douglas C. Ravenel

Trans. Amer. Math. Soc. 347 (1995), 3473-3502

DOI: https://doi.org/10.1090/S0002-9947-1995-1297530-2

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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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