#### Volume 8, issue 4 (2008)

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The homotopy of $\mathit{MString}$ and $\mathit{MU}\langle 6\rangle$ at large primes

### Mark Hovey

Algebraic & Geometric Topology 8 (2008) 2401–2414
##### Abstract

We use Hopf rings to compute the homotopy rings ${\pi }_{\ast }MO〈8〉$ and ${\pi }_{\ast }MU〈6〉$ at primes $>3$. In this case, the additive structure is well-known, but the ring structure is not polynomial. Instead, these rings are quotients of polynomial rings by infinite regular sequences.

##### Keywords
bordism, cobordism, String manifold, String bordism, Hopf ring
##### Mathematical Subject Classification 2000
Primary: 55N22
Secondary: 57R90, 55R45