multiplicative cohomology theories precise, May, Quinn, Ray, and Tornehave [@MQRT:ersers] developed the notion of an ${E_{\infty}}$ ring spectrum and used it to describe the obstruction theory for orientations of spherical fibrations. Indeed the Thom spectra of infinite Grassmannians such as $BO$ and $BU$ provided their starting examples of ${E_{\infty}}$ ring spectra. It is interesting to recall that the theory of structured ring spectra and “brave new algebras” in part had roots in this extremely concrete geometric theory.

In a forthcoming paper, three of us (Ando, Hopkins, Rezk) construct an ${E_{\infty}}$ orientation of $tmf$, the spectrum of topological modular forms [@Hopkins:icm2002; @AHR:orientation]: more precisely, we construct a map of ${E_{\infty}}$ ring spectra from the Thom spectrum $MO\langle 8
\rangle$, also known as $MString$, to the spectrum $tmf$. That paper requires a formulation of the obstruction theory of [@MQRT:ersers] in terms of the adjoint relationship between units and ${{\Sigma^{\infty}}_{+}}{\Omega^{\infty}}$ described in Theorem \[t-th-units-intro\] below. It also requires a formulation of the obstruction theory in terms of modern topological or simplicial model categories of ${E_{\infty}}$ ring spectra.

This paper began as an effort to connect the results in [@MQRT:ersers] to the results required by [@AHR:orientation]. In the course of doing this, we realized 