in light of their categories of parametrized spectra. Very recently May has prepared an authoritative paper revisiting operad (ring) spaces and operad (ring) spectra from a modern perspective, which has substantial overlap with some of the discussion in this paper [@May:rant] (notably Section \[sec:constr-may-quinn\]).

Acknowledgments
---------------

We thank Peter May for his many contributions to this subject and for useful conversations and correspondence. We are also very grateful to Mike Mandell for invaluable help with many parts of this project. We thank Jacob Lurie for helpful conversations and encouragement. We thank John Lind for pointing out an error in a previous draft. Some of the results in Section \[sec:ainfty-thom-spectrum\] are based on work in the 2005 University of Chicago Ph.D. thesis of the second author: he would like to particularly thank his advisors, May and Mandell, for all of their assistance.

Overview {#sec:introduction}
========

In this section, we give a detailed summary of the contents of the paper and state the main results.

The spectrum of units and ${E_{\infty}}$ orientations {#sec:obstr-theory-einfty}
-----------------------------------------------------

We begin in §\[sec:constr-may-quinn\] by revisiting the construction, due to May et al. [@MQRT:ersers], of the spectrum of units ${{gl_{1}}R}$ associated to an ${E_{\infty}}$ ring spectrum $R.$ Motivated 