arXiv:0908.1092 Diagram spaces, diagram spectra, and spectra of units from arXiv Front: math.AT by John Lind 1 person liked this We compare the infinite loop spaces associated to symmetric spectra, orthogonal spectra, and EKMM S-modules. Each of these categories of structured spectra has a corresponding category of structured spaces that receives the infinite loop space functor \Omega^\infty. We prove that these models for spaces are Quillen equivalent and that the infinite loop space functors \Omega^\infty agree. This comparison is then used to show that two different constructions of the spectrum of units gl_1 R of a structured ring spectrum R agree.
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