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