## Realizing Commutative Ring Spectra as E∞ Ring Spectra (1999)

Citations: | 7 - 2 self |

### BibTeX

@TECHREPORT{Goerss99realizingcommutative,

author = {P. G. Goerss and M. J. Hopkins},

title = {Realizing Commutative Ring Spectra as E∞ Ring Spectra},

institution = {},

year = {1999}

}

### OpenURL

### Abstract

We outline an obstruction theory for deciding when a homotopy commutative and associative ring spectrum is actually an E∞ ring spectrum. The obstruction groups are André-Quillen cohomology groups of an algebra over an E∞ operad. The same cohomology theory is part of a spectral sequence for computing the homotopy type of mapping spaces between E∞ ring spectrum. The obstruction theory arises out of techniques of Dwyer, Kan, and Stover, and the main application here is to prove an analog of a theorem of Haynes Miller and the second author: the Lubin-Tate spectra En are E∞ and the space of E∞ self-maps has weakly contractible components.