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

Abstract

We use Hopf rings to compute the homotopy rings ${\pi }_{\ast }MO\langle 8\rangle$ and ${\pi }_{\ast }MU\langle 6\rangle$ 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.