Multiplicative Equivariant Thom Spectra & Structured Real Orientations

Ryan Quinn, Qi Zhu

For strongly even ${\mathbb{E}}_{\infty }^{C_2}$-rings $E$ we show that any homotopy ring map $\mathrm{MU}\to E^e$ lifts to an ${\mathbb{E}}_{\ddot{I}}$-map ${\mathrm{MU}}_{\mathbb{R}}\to E$. T…