En Genera

Let $R$ be an $E_{2}$ ring spectrum with zero odd dimensional homotopy groups.  Every map of ring spectra $MU\to R$ is represented by a map of $E_{2}$ ring spectra.  If $2$ is invertible in $\pi_{0}R$, then every map of ring spectra $MSO\to R$ is represented by a map of $E_{2}$ ring spectra.  Joint work with Greg Chadwick.

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